### Rick Lyons (@Rick Lyons)

Richard Lyons is a Contracting Systems Engineer and Lecturer at Besser Associates, Mountain View, Calif. He has written over 30 articles and conference papers on DSP topics, and authored Amazon.com's top selling DSP book "Understanding Digital Signal Processing, 3rd Ed.". He served as an Associate Editor at IEEE Signal Processing Magazine, for nine years, where he created and edited the "DSP Tips & Tricks" column. Lyons is the editor of, and contributor to, the book "Streamlining Digital Signal Processing-A Tricks of the Trade Guidebook, 2nd Ed." (Wiley & Sons, 2012).

## A New Contender in the Quadrature Oscillator Race

This blog advocates a relatively new and interesting quadrature oscillator developed by A. David Levine in 2009 and independently by Martin Vicanek in 2015 [1]. That oscillator is shown in Figure 1.

The time domain equations describing the Figure 1 oscillator are

w(n) =...

## A DSP Quiz Question

Here's a DSP Quiz Question that I hope you find mildly interesting

BACKGROUND

Due to the periodic natures an N-point discrete Fourier transform (DFT) sequence and that sequence’s inverse DFT, it is occasionally reasonable to graphically plot either of those sequences as a 3-dimensional (3D) circular plot. For example, Figure 1(a) shows a length-32 x(n) sequence with its 3D circular plot given in Figure 1(b).

HERE'S THE QUIZ QUESTION:

I was reading a paper by an audio DSP engineer where the...

## An Efficient Full-Band Sliding DFT Spectrum Analyzer

In this blog I present two computationally efficient full-band discrete Fourier transform (DFT) networks that compute the 0th bin and all the positive-frequency bin outputs for an N-point DFT in real-time on a sample-by-sample basis.

An Even-N Spectrum Analyzer

The full-band sliding DFT (SDFT) spectrum analyzer network, where the DFT size N is an even integer, is shown in Figure 1(a). The x[n] input sequence is restricted to be real-only valued samples. Notice that the only real parts of...

## A Simpler Goertzel Algorithm

February 4, 2021

In this blog I propose a Goertzel algorithm that is simpler than the version of the Goertzel algorithm that is traditionally presented DSP textbooks. Below I very briefly describe the DSP textbook version of the Goertzel algorithm followed by a description of my proposed simpler algorithm.

The Traditional DSP Textbook Goertzel Algorithm

The so-called Goertzel algorithm is used to efficiently compute a single mth-bin sample of an N-point discrete Fourier transform (DFT) [1-4]. The...

## 60-Hz Noise and Baseline Drift Reduction in ECG Signal Processing

Electrocardiogram (ECG) signals are obtained by monitoring the electrical activity of the human heart for medical diagnostic purposes [1]. This blog describes a very efficient digital filter used to reduce both 60 Hz AC power line noise and unwanted signal baseline drift that often contaminate ECG signals.

PDF_HERE

We'll first describe the ECG noise reduction filter and then examine the filter's performance in a real-world ECG signal filtering example.Proposed ECG Noise Reduction Digital...

## A Fast Real-Time Trapezoidal Rule Integrator

This blog presents a computationally-efficient network for computing real‑time discrete integration using the Trapezoidal Rule.

Background

While studying what is called "N-sample Romberg integration" I noticed that such an integration process requires the computation of many individual smaller‑sized integrations using the Trapezoidal Rule integration method [1]. My goal was to create a computationally‑fast real‑time Trapezoidal Rule integration network to increase the processing...

## A Beginner's Guide To Cascaded Integrator-Comb (CIC) Filters

This blog discusses the behavior, mathematics, and implementation of cascaded integrator-comb filters.

Cascaded integrator-comb (CIC) digital filters are computationally-efficient implementations of narrowband lowpass filters, and are often embedded in hardware implementations of decimation, interpolation, and delta-sigma converter filtering.

After describing a few applications of CIC filters, this blog introduces their structure and behavior, presents the frequency-domain...

## The DFT of Finite-Length Time-Reversed Sequences

Recently I've been reading papers on underwater acoustic communications systems and this caused me to investigate the frequency-domain effects of time-reversal of time-domain sequences. I created this blog because there is so little coverage of this topic in the literature of DSP.

This blog reviews the two types of time-reversal of finite-length sequences and summarizes their discrete Fourier transform (DFT) frequency-domain characteristics.

The Two Types of Time-Reversal in DSP

...

## Update To: A Wide-Notch Comb Filter

December 9, 2019

This blog presents alternatives to the wide-notch comb filter described in Reference [1]. That comb filter, which for notational reasons I now call a 2-RRS wide notch comb filter, is shown in Figure 1. I use the "2-RRS" moniker because the comb filter uses two recursive running sum (RRS) networks.

The z-domain transfer function of the 2-RRS wide-notch comb filter, H2-RRS(z), is:

References

[1] R. Lyons, "A Wide-Notch Comb Filter", dsprelated.com Blogs, Nov. 24, 2019, Available...

## A Wide-Notch Comb Filter

This blog describes a linear-phase comb filter having wider stopband notches than a traditional comb filter.

Background

Let's first review the behavior of a traditional comb filter. Figure 1(a) shows a traditional comb filter comprising two cascaded recursive running sum (RRS) comb filters. Figure 1(b) shows the filter's co-located dual poles and dual zeros on the z-plane, while Figure 1(c) shows the filter's positive-frequency magnitude response when, for example, D = 9. The...

## The Risk In Using Frequency Domain Curves To Evaluate Digital Integrator Performance

This blog shows the danger in evaluating the performance of a digital integration network based solely on its frequency response curve. If you plan on implementing a digital integrator in your signal processing work I recommend you continue reading this blog.

Background

Typically when DSP practitioners want to predict the accuracy performance of a digital integrator they compare how closely that integrator's frequency response matches the frequency response of an ideal integrator [1,2]....

## Reduced-Delay IIR Filters

This blog gives the results of a preliminary investigation of reduced-delay (reduced group delay) IIR filters based on my understanding of the concepts presented in a recent interesting blog by Steve Maslen [1].

Development of a Reduced-Delay 2nd-Order IIR Filter

Maslen's development of a reduced-delay 2nd-order IIR filter begins with a traditional prototype filter, HTrad, shown in Figure 1(a). The first modification to the prototype filter is to extract the b0 feedforward coefficient...

## Somewhat Off Topic: Deciphering Transistor Terminology

I recently learned something mildly interesting about transistors, so I thought I'd share my new knowledge with you folks. Figure 1 shows a p-n-p transistor comprising a small block of n-type semiconductor sandwiched between two blocks of p-type semiconductor.

The terminology of "emitter" and "collector" seems appropriate, but did you ever wonder why the semiconductor block in the center is called the "base"? The word base seems inappropriate because the definition of the word base is:...

## Reducing IIR Filter Computational Workload

This blog describes a straightforward method to significantly reduce the number of necessary multiplies per input sample of traditional IIR lowpass and highpass digital filters.

Reducing IIR Filter Computations Using Dual-Path Allpass Filters

We can improve the computational speed of a lowpass or highpass IIR filter by converting that filter into a dual-path filter consisting of allpass filters as shown in Figure 1.

...

## A Lesson In Engineering Humility

Let's assume you were given the task to design and build the 12-channel telephone transmission system shown in Figure 1.

Figure 1

At a rate of 8000 samples/second, each telephone's audio signal is sampled and converted to a 7-bit binary sequence of pulses. The analog signals at Figure 1's nodes A, B, and C are presented in Figure 2.

Figure 2

I'm convinced that some of you subscribers to this dsprelated.com web site could accomplish such a design & build task....

## Controlling a DSP Network's Gain: A Note For DSP Beginners

This blog briefly discusses a topic well-known to experienced DSP practitioners but may not be so well-known to DSP beginners. The topic is the proper way to control a digital network's gain. Digital Network Gain Control Figure 1 shows a collection of networks I've seen, in the literature of DSP, where strict gain control is implemented.

FIGURE 1. Examples of digital networks whose initial operations are input signal...

## Stereophonic Amplitude-Panning: A Derivation of the 'Tangent Law'

In a recent Forum post here on dsprelated.com the audio signal processing subject of stereophonic amplitude-panning was discussed. And in that Forum thread the so-called "Tangent Law", the fundamental principle of stereophonic amplitude-panning, was discussed. However, none of the Forum thread participants had ever seen a derivation of the Tangent Law. This blog presents such a derivation and if this topic interests you, then please read on.

The notion of stereophonic amplitude-panning is...

## A Brief Introduction To Romberg Integration

This blog briefly describes a remarkable integration algorithm, called "Romberg integration." The algorithm is used in the field of numerical analysis but it's not so well-known in the world of DSP.

To show the power of Romberg integration, and to convince you to continue reading, consider the notion of estimating the area under the continuous x(t) = sin(t) curve based on the five x(n) samples represented by the dots in Figure 1.

The results of performing a Trapezoidal Rule, a...

## Microprocessor Family Tree

Below is a little microprocessor history. Perhaps some of the ol' timers here will recognize a few of these integrated circuits. I have a special place in my heart for the Intel 8080 chip.

Image copied, without permission, from the now defunct Creative Computing magazine, Vol. 11, No. 6, June 1985.

## Two Easy Ways To Test Multistage CIC Decimation Filters

This blog presents two very easy ways to test the performance of multistage cascaded integrator-comb (CIC) decimation filters [1]. Anyone implementing CIC filters should take note of the following proposed CIC filter test methods.

Introduction

Figure 1 presents a multistage decimate by D CIC filter where the number of stages is S = 3. The '↓D' operation represents downsampling by integer D (discard all but every Dth sample), and n is the time index.

If the Figure 3 filter's...

## FFT Interpolation Based on FFT Samples: A Detective Story With a Surprise Ending

This blog presents several interesting things I recently learned regarding the estimation of a spectral value located at a frequency lying between previously computed FFT spectral samples. My curiosity about this FFT interpolation process was triggered by reading a spectrum analysis paper written by three astronomers [1].

My fixation on one equation in that paper led to the creation of this blog.

Background

The notion of FFT interpolation is straightforward to describe. That is, for example,...

## An Efficient Linear Interpolation Scheme

This blog presents a computationally-efficient linear interpolation trick that requires at most one multiply per output sample.

Background: Linear Interpolation

Looking at Figure 1(a) let's assume we have two points, [x(0),y(0)] and [x(1),y(1)], and we want to compute the value y, on the line joining those two points, associated with the value x.

Figure 1: Linear interpolation: given x, x(0), x(1), y(0), and y(1), compute the value of y. ...

## Online DSP Classes: Why Such a High Dropout Rate?

Last year the IEEE Signal Processing Magazine published a lengthy article describing three university-sponsored online digital signal processing (DSP) courses [1]. The article detailed all the effort the professors expended in creating those courses and the courses' perceived values to students.

However, one fact that struck me as important, but not thoroughly addressed in the article, was the shocking dropout rate of those online courses. For two of the courses the article's...

## Errata for the book: 'Understanding Digital Signal Processing'

Errata 3rd Ed. International Version.pdfErrata 3rd Ed. International Version.pdf

This blog post provides, in one place, the errata for each of the many different Editions/Printings of my book Understanding Digital Signal Processing.

If you would like the errata for your copy of the book, merely scroll down and click on the appropriate red line below. For the American versions of the various Editions of the book you'll need to know the "Printing Number" of your copy of the...

## Above-Average Smoothing of Impulsive Noise

In this blog I show a neat noise reduction scheme that has the high-frequency noise reduction behavior of a traditional moving average process but with much better impulsive-noise suppression.

In practice we may be required to make precise measurements in the presence of highly-impulsive noise. Without some sort of analog signal conditioning, or digital signal processing, it can be difficult to obtain stable and repeatable, measurements. This impulsive-noise smoothing trick,...

## Looking For a Second Toolbox? This One's For Sale

June 29, 2017
In case you're looking for a second toolbox, this used toolbox is for sale.

The blue-enameled steel toolbox measures 13 x 7 x 5 inches and, when opened, has a three-section tray attached to the lid. Showing signs of heavy use, the interior, tray, and exterior have collected a fair amount of dirt and grease and bear many scratches. The bottom of the box is worn from having been slid on rough surfaces.

The toolbox currently resides in Italy. But don't worry, it can be shipped to you....

## Sinusoidal Frequency Estimation Based on Time-Domain Samples

The topic of estimating a noise-free real or complex sinusoid's frequency, based on fast Fourier transform (FFT) samples, has been presented in recent blogs here on dsprelated.com. For completeness, it's worth knowing that simple frequency estimation algorithms exist that do not require FFTs to be performed . Below I present three frequency estimation algorithms that use time-domain samples, and illustrate a very important principle regarding so called "exact"...

## Frequency Translation by Way of Lowpass FIR Filtering

Some weeks ago a question appeared on the dsp.related Forum regarding the notion of translating a signal down in frequency and lowpass filtering in a single operation [1]. It is possible to implement such a process by embedding a discrete cosine sequence's values within the coefficients of a traditional lowpass FIR filter. I first learned about this process from Reference [2]. Here's the story.

Traditional Frequency Translation Prior To Filtering

Think about the process shown in...

## The Real Star of Star Trek

Unless you've been living under a rock recently, you're probably aware that this month is the 50-year anniversary of the original Star Trek show on American television. It's an anniversary worth noting, as did Time and Newsweek magazines with their special editions.

Over the years I've come to realize that a major star of the original Star Trek series wasn't an actor. It was a thing. The starship USS Enterprise! Before I explain my thinking, here's a little...

## An s-Plane to z-Plane Mapping Example

While surfing around the Internet recently I encountered the 's-plane to z-plane mapping' diagram shown in Figure 1. At first I thought the diagram was neat because it's a good example of the old English idiom: "A picture is worth a thousand words." However, as I continued to look at Figure 1 I began to detect what I believe are errors in the diagram.

Reader, please take a few moments to see if you detect any errors in Figure 1.

...

## Should DSP Undergraduate Students Study z-Transform Regions of Convergence?

Not long ago I presented my 3-day DSP class to a group of engineers at Tektronix Inc. in Beaverton Oregon [1]. After I finished covering my material on IIR filters' z-plane pole locations and filter stability, one of the Tektronix engineers asked a question similar to:

"I noticed that you didn't discuss z-plane regions of      convergence here. In my undergraduate DSP class we      spent a lot of classroom and homework time on the  ...

## Implementing Impractical Digital Filters

This blog discusses a problematic situation that can arise when we try to implement certain digital filters. Occasionally in the literature of DSP we encounter impractical digital IIR filter block diagrams, and by impractical I mean block diagrams that cannot be implemented. This blog gives examples of impractical digital IIR filters and what can be done to make them practical.

Implementing an Impractical Filter: Example 1

Reference [1] presented the digital IIR bandpass filter...

## An Astounding Digital Filter Design Application

I've recently encountered a digital filter design application that astonished me with its design flexibility, capability, and ease of use. The software is called the "ASN Filter Designer." After experimenting with a demo version of this filter design software I was so impressed that I simply had publicize it to the subscribers here on dsprelated.com.

What I Liked About the ASN Filter Designer

With typical filter design software packages the user enters numerical values for the...

## The Swiss Army Knife of Digital Networks

This blog describes a general discrete-signal network that appears, in various forms, inside so many DSP applications.

Figure 1 shows how the network's structure has the distinct look of a digital filter—a comb filter followed by a 2nd-order recursive network. However, I do not call this useful network a filter because its capabilities extend far beyond simple filtering. Through a series of examples I've illustrated the fundamental strength of this Swiss Army Knife of digital networks...

## Digital Envelope Detection: The Good, the Bad, and the Ugly

Recently I've been thinking about the process of envelope detection. Tutorial information on this topic is readily available but that information is spread out over a number of DSP textbooks and many Internet web sites. The purpose of this blog is to summarize various digital envelope detection methods in one place.

Here I focus on envelope detection as it is applied to an amplitude-fluctuating sinusoidal signal where the positive-amplitude fluctuations (the sinusoid's envelope)...

## A Useful Source of Signal Processing Information

I just discovered a useful web-based source of signal processing information that was new to me. I thought I'd share what I learned with the subscribers here on DSPRelated.com.

The Home page of the web site that I found doesn't look at all like it would be useful to us DSP fanatics. But if you enter some signal processing topic of interest, say, "FM demodulation" (without the quotation marks) into the 'Search' box at the top of the web page

and click the red 'SEARCH...

## Optimizing the Half-band Filters in Multistage Decimation and Interpolation

This blog discusses a not so well-known rule regarding the filtering in multistage decimation and interpolation by an integer power of two. I'm referring to sample rate change systems using half-band lowpass filters (LPFs) as shown in Figure 1. Here's the story.

Figure 1: Multistage decimation and interpolation using half-band filters.

Multistage Decimation – A Very Brief Review

Figure 2(a) depicts the process of decimation by an integer factor D. That...

## Implementing Simultaneous Digital Differentiation, Hilbert Transformation, and Half-Band Filtering

Recently I've been thinking about digital differentiator and Hilbert transformer implementations and I've developed a processing scheme that may be of interest to the readers here on dsprelated.com.

This blog presents a novel method for simultaneously implementing a digital differentiator (DD), a Hilbert transformer (HT), and a half-band lowpass filter (HBF) using a single tapped-delay line and a single set of coefficients. The method is based on the similarities of the three N =...

## A New Contender in the Digital Differentiator Race

This blog proposes a novel differentiator worth your consideration. Although simple, the differentiator provides a fairly wide 'frequency range of linear operation' and can be implemented, if need be, without performing numerical multiplications.

Background

In reference [1] I presented a computationally-efficient tapped-delay line digital differentiator whose $h_{ref}(k)$ impulse response is:

$$h_{ref}(k) = {-1/16}, \ 0, \ 1, \ 0, \ {-1}, \ 0, \ 1/16 \tag{1}$$

and...

## The Most Interesting FIR Filter Equation in the World: Why FIR Filters Can Be Linear Phase

This blog discusses a little-known filter characteristic that enables real- and complex-coefficient tapped-delay line FIR filters to exhibit linear phase behavior. That is, this blog answers the question:

What is the constraint on real- and complex-valued FIR filters that guarantee linear phase behavior in the frequency domain?

I'll declare two things to convince you to continue reading.

Declaration# 1: "That the coefficients must be symmetrical" is not a correct

## Four Ways to Compute an Inverse FFT Using the Forward FFT Algorithm

July 7, 20151 comment

If you need to compute inverse fast Fourier transforms (inverse FFTs) but you only have forward FFT software (or forward FFT FPGA cores) available to you, below are four ways to solve your problem.

Preliminaries To define what we're thinking about here, an N-point forward FFT and an N-point inverse FFT are described by:

## Re: DSP principles question

Hi Rich. Your notion that "we mathematically can fiddle the apparent sampling rate, perhaps by interpolation/decimation or some such" to change the sample rate of...

## Re: DSP principles question

Hello richgroot. Can you tell what page, of which edition, of my book is causing you problems?

## Re: Real Numbers

Hi Cedron. Regarding the proof I copied from the Internet and posted here, you wrote: "Rick's "proof" is the geometric sum series. The only thing missing was to...

## Re: Real Numbers

Hi bholzmayer. Thanks for your interesting thoughts!

## Re: Real Numbers

Hi Cedron. I'm pretty sure I understand what the number zero means. But I'm not confident that I fully understand what infinity means.I vaguely recall several years...

## Re: Real Numbers

Hello LM741. I'm not familiar with hyper reals. Also, I'm afraid that if I study those numbers I will experience hypertension.

## Re: Real Numbers

Hi Jason (jms_nh). I don't recall what caused me to visit Keith Enevoldsen's web site. I liked his "embedded ovals" diagram. So I copied that diagram, used his text,...

Real Numbers.jpg

## Re: Restorative Up-Sampling (RUP) and Quantization Error and Artifact Reduction (QEAR)

Hi Winkie. Below is my original .wav file (Capt Kirk saying, "Not chess Mr. Spock".):Capt_Kirk_Original.wavBelow is the original file decimated by a factor of eight:Capt_Kirk_Decimated_by_eight.wavAfter...

## Re: Restorative Up-Sampling (RUP) and Quantization Error and Artifact Reduction (QEAR)

Hi Winkie. I ran your MATLAB code but the following command gave me an error:  XX = F((N):((2*N)));So I changed that command to:  XX = F((N):((2*N-1)));Was my...

## Re: Restorative Up-Sampling (RUP) and Quantization Error and Artifact Reduction (QEAR)

Hi Winkie. I see your MATLAB code for your function 'A = rup(x,v)'. Can you tell use something about the variables 'x', 'v', and the output 'A'? That is, given 'x'...

## Re: Restorative Up-Sampling (RUP) and Quantization Error and Artifact Reduction (QEAR)

Hi Winkie. By any chance would you have MATLAB code that implements your RUP and QEAR processes that you would be willing to share with us?

## Re: Matlab Basic Functions Reference (pdf)

Hi Neil.Thanks for providing the link to the useful PDF file.

## Re: Confusion understanding some equations in the book "Understanding Digital Signal Processing" (Indian edition).

Hi adaptive filter. Shoot! You are correct. I have changed my Dec 6 reply's text to:"The phases of the positive-amplitude spectral values in Figure 3-9(a) are zero...

## Re: PLL fun : some personnal work that I'd like to share

Hi pylessard. Is the a tutorial web page we can read to help us understand what we're looking at when we visit your "PLL Application" web page?

## Re: Confusion understanding some equations in the book "Understanding Digital Signal Processing" (Indian edition).

Hello bittersweet. Thank you for your kind words. If you are a computer science student then I have a question for you.Question:How many software programmers does...

## Re: Confusion understanding some equations in the book "Understanding Digital Signal Processing" (Indian edition).

Hello bittersweet. (I'm replying to your Dec. 6, 2020 post.) Let's settle one thing right now. You may think you're asking a "dumb" question. Believe me, there...

## Re: How to synthesize band-limited noise?

Hello Marcinstein. Oh no no! I'm not in the same league as Charles Rader and fred harris. Charles Rader, among his other accomplishments, is literally one...

## Re: Purity > 1?

Hi Aaron45. OK. So when a single input sinusoid's frequency is not at an N-point DFT's bin center then all of the DFT's N magnitude samples will be nonzero  Then...

## Re: Purity > 1?

Hi Aaron45. I think of the numerical-error accumulation as being caused by the fact that we cannot place the Goertzel network's poles *exactly* at the desired angles...

## Re: Purity > 1?

Hi Aaron45. I see what's happening here!The version of Parseval's Theorem that applies to digital signal processing is:Σ(x[n])^2 = 1/N*Σ(|X[m]|)^2        ...

## Re: Purity > 1?

Aaron45, are you using 64-bit numerical values in your computations? Also, what is the nature of your input test signal?

## Re: Has any one seen this window function?

Hi Cedron. I've not seen that w[n] window sequence before. It's frequency-domain behavior is super-similar to the Von Hann (hanning) window if we ignoring w[n]'s...

## Re: Has any one seen this window function?

Hi kaz. Whether or not a boxcar (rectanglar) sequence is a window depends on your definition of the word "window".

## Re: Parallel CIC filter processing enquiry

Hi kaz.I think you're correct. I figured any DC component of the original analog signal will exist as a DC component of any decimated sequence. But if each data...

## Re: Parallel CIC filter processing enquiry

clear, clcNum_Samples = 80; % Number of input time samplesN = 8;% DFT sizen = 0:Num_Samples-1;Fs = 1000; % Sample rate in HzFo = 50; % Input sinusoid's frequency%%%%%%%%%%%%%%%%%%%%%%Generate...

## Re: Parallel CIC filter processing enquiry

Hi Phil_SG. You wrote: "The data is split across 5 parallel, 16 bit samples." What does that exactly mean? Can you post a diagram showing data split across 5 parallel...

## Re: Question regarding CIC filter

Hi aminnoura. If you have questions regarding the "A Beginner's Guide to Cascaded Integrator-Comb Filters" blog, I am willing to try to answer you questions.

## Re: Question regarding CIC filter

Hi aminnoura.I'm not an expert on digital communications systems but if your signal can only have four values then it appears to me that your signal may be "symbols"...

## Re: Matlab, properly using IFFT, FIR Filter Desing

Hello Jim.Ha ha. Don't worry. The discrete time domain is, every now and then, mysterious to us all.

## Re: Who discovered the math of the digital polar discriminator?

Hi Gsparky2004. I think napierm is correct. I searched my copy of Frerking's book and the Section titled "Digital Differentiation" goes from page 253 to 257. I...

## Re: New quiz question by Rick Lyons

Hello Marcin. My my. Thank you. Your words are too kind! I'm happy that my DSP book has been of some value to you. Marcin, below are two web pages that might interest...

## Re: New quiz question by Rick Lyons

Hi Marcinstein. Yes. Only one question.

## Re: Difference amplitude (x[n] - y[n-1]) quantization in first order iir

Hi max3031.I don't know what you mean by quantizing the "difference amplitude term (x[n] - y[n-1])". But I would like to say:If I'm not mistaken your IIR filter...

## Re: Setting 25KHz playback sampling rate in sound card

Hi David (dgshaw6). That's quite a story you tell. You certainly did work with some signal processing "heavyweights". Thanks for the Farrow paper. I'm going to...

## Re: Why complex numbers are used/introduced in electricity

Hi Sara. Complex numbers prove the puzzling idea that the product of two negative numbers is a positive number. Have you ever seen this poem:   A minus times...

## Re: Setting 25KHz playback sampling rate in sound card

Hi David. Thanks. Wow, that's quite a resume!I've run a cross papers that mention Farrow filters, but I've never actually studied those filters. I went to the IEEE...

...

## Re: Why complex numbers are used/introduced in electricity

Hi Sara. A few words from me (for whatever they are worth):Complex numbers are important because they have a powerful mathematical relationship with the trigonometric...

## Re: Setting 25KHz playback sampling rate in sound card

Hi dgshaw6. Interesting! What company did you work for?

## Re: Setting 25KHz playback sampling rate in sound card

Hi gaurav_lohiya. It seems to me that you should downsample your IF signal BEFORE you perform AM demodulation.

## Re: Moving average followed by a decimator.

Hello Maurizio_Malaspina. I'm not sure if it's true but I think you may implementing what is called a cascaded integrator-comb (CIC) filter. If that's true, please...

## Re: Sampling and using the data

Hi kimfmx. You wrote: "2) The bandwidth of 1.92Mhz is way too much information, and I need to filter out excess noise and signals out of my bandwidth, so ill have...

## Re: What does filtering do to a signal in time domain? Does the signal gets distorted?

Hi amitjonak. Again, I'm no expert on digital radio systems and I do not fully understand some of the "Replies" here in this thread, but I'll mention one more idea...

## Re: Sampling and using the data

Hi kimfmx. First, someone here will be able to answer all of your questions. But to do so we need to know EXACTLY what is the nature of your signals at EACH stage...

## Re: What does filtering do to a signal in time domain? Does the signal gets distorted?

Hi amitjonak. I'm no expert on digital radio systems but I'll mention a few ideas here. In digital radio, a transmitter's filter that converts "symbols" (numbers)...

## Re: FIR allpass with desired group delay

Hi. UliBru. MATLAB has a 'fir2()' command that designs FIR filters having arbitrary frequency responses. If you have MATLAB software you might try using its 'fir2()'...

## Re: FIR allpass with desired group delay

Hi UliBry. Your filter's phase plot (your first plot) seems strange to me. I expected your 2nd-order allpass filter to have phase values of:   zero radians...

## Re: FIR allpass with desired group delay

Hello UliBru. It would help if you posted a frequency-domain drawing of the desired group delay of your allpass filter. If you do that, label the freq axis in terms...

## Re: FIR filtering vs linear convolution

Hello chaitanya02.Just so you know, the convolution of your 'h' and 'x' sequences is:[1, 4, 10, 20, 25, 24, 16, 0, 0, 0, 0, 0, 0].The convolution of two seven-sample...

## Re: DTFT, plotting with various sampling frequencies

Hi transient. You cannot derive the DTFT equation for your continuous xa(t) signal. We can only derive the DTFT equations for discrete sequences. I derived the DTFT...

## Re: DTFT, plotting with various sampling frequencies

Hi transient. You cannot compute continuous-time or discrete-time Fourier transforms using a computer. In those transforms the frequency variable is continuous,...

## Re: Inverse FFT of a Sampled Frequency Domain Function

Hi jleman.Assumming your FFT software only works when the number of time samples is an integer power of two, perform the following test:(1) Make sure your original...

## Re: Need tutorial information on 8VSB modulation

Hi Eric.You "came through" again!  Thanks a lot.

## Re: Need tutorial information on 8VSB modulation

Hi Eric. Quadrature demodulator huh? That answers one of my questions. Thanks for the information!!

## Need tutorial information on 8VSB modulation

Hi. I've been trying to learn the technical details of 8VSB modulation (and demodulation) used in North America's digital television broadcasts.  But the only material...

## Re: Expect Downtime

Hello doneill.  Neat!  Thanks for all the information.  And I agree, "Avoid windowed sampling for A/D converter testing."

## Re: Expect Downtime

Hello Doneill.The image you posted looks interesting. What is it? Thanks.

## Re: #CIC filters and testing them

Hi ChuckMcM.Regarding the 2nd paragraph of your latest Comment that begins with "[Side note:...", the "arrow into z−1 block combined with the z-1 block" are not...

## Re: #CIC filters and testing them

Hi ChuckMcM.If I understand your latest Comment that begins with "There is certainly something...", it seems to me you are implementing your first comb filter (Co0)...

## Re: #CIC filters and testing them

Hi ChuckMcM.Below is my listing of the integrators/differentiators outputs for a 3-stage decimate-by-5 CIC decimator.The impulse response output of the 3rd differentiator...

## Re: #CIC filters and testing them

Hi ChuckMcM. It's 1:40 AM on Jan. 12 for me right now. Let me dig through my old MATLAB code to see how the outputs of my integrators/differentiators compare with...

## What is the cost of a typical MSEE degree?

Hi. Recently I received an e-mail from the Coursera online education web site announcing a new online Masters of Science Degree in Electrical Engineering (MSEE)...

## Re: Guaranteed stable sliding Goertzel implementation

Hi gretzteam. That "An Accurate and Stable Sliding DFT Computed by a Modified CIC Filter" article was printed in the magazine's 'DSP Tips & Tricks' column. When...

## Re: Moving average filter using Blockram

Adira. The frequency magnitude responses of running sum filters do not have a flat passband. Their freq magnitude responses look like the following: The kind of...

## Re: Moving average filter using Blockram

Adira. In the world of DSP the word "bandwidth" is a single number measured in Hz. For example, human speech signals are said to have a bandwidth of 4 kHz. (Notice...

## Re: Moving average filter using Blockram

Hello Adira.Your terminology confuses me. I do not know what your words "Reconstructed signal frequencies range =0-3khz" or "Bandwidth of at least 0-20khz" mean.You...

## Re: Moving average filter using Blockram

Hi Adira. The expression:is a "nonrecursive N-sample moving summation". If you divided each y[n] output sample by N then it would be an "nonrecursive N-sample moving...

## Re: Moving average filter using Blockram

Hi Adira. Your equation:y(n)=y(n-1)+x(n)+x(n-N)is not correct. It should be:y(n) = y(n-1) + x(n)-x(n-N)But the corrected equation is not an averager, it's what is...

## Re: Guaranteed stable sliding Goertzel implementation

Hi KimT. Here are a few papers that discuss ways to implement stable sliding DFTs: Denis A. Gudovskiy and Lichung Chu, "An Accurate and Stable Sliding DFT Computed...

## Re: ADC and Complex Mixer Nyquist question

Hi omersayli. Here is what I'm saying:The following is the spectrum of the real-valued x(n) sequence.If I performed passband filtering of the x(n) sequence to attenuate...

## Re: ADC and Complex Mixer Nyquist question

Hi omersayli.First, we don't "shift the spectrum to the fc and -fc". We shift X(m)'s spectrum in the negative-frequency direction by fc Hz. What I hoped to convey...

## Re: ADC and Complex Mixer Nyquist question

Hi sachinwannabe.Let's say the output of your ADC (Fs sampling rate of one GHz) is a real-valued x(n) sequence whose |X(m)| FFT spectral magnitude is shown below...

## Re: New IEEE Signal Processing Society Journal

Hi Stephane.I've always thought that dsprelated.com was "aimed at practicing engineers".

## Re: New IEEE Signal Processing Society Journal

Hi Y(J)S. Ah ha. Thanks.

## Re: New IEEE Signal Processing Society Journal

Hi Y(J)S. What is "PNAS"?

## New IEEE Signal Processing Society Journal

The IEEE Signal Processing Society (SPS) is starting a new publication program called the "IEEE Open Journal of Signal Processing". That program will be "dedicated...

## Re: amplitude of passband frequencies in FIR bandpass filter

Hi naumankalia. Perhaps the material at the following link will be of some use to you:https://www.dsprelated.com/showcode/263.php

## Re: concept of bandwidth

Hi Sharan123.When you write: "...for modulation at rate r1"I have no idea what you mean. No idea at all. I think you may be confusing the two concepts of "spectral...

## Re: concept of bandwidth

Hi Sharan123. We have a terminology problem here. In your Oct. 23 Comment, when you use the word "rate" I assume you mean "sample rate." And 'sample rates' are measured...

## Re: concept of bandwidth

Hi Sharan123.I'm sorry. I don't know what your words "read out" mean.

## Re: concept of bandwidth

Hi Sharan123. I'm replying to your second Oct. 22 "Reply."If your phrase "bandwidth" is related to the frequency-domain bandwidth of a time-domain sampled sequence,...

## Re: concept of bandwidth

Hi Greg. Ah ha, OK. Thanks.

## Re: A question regarding MATLAB's 'invfreqz()' command

Hi omersayli. Please call me "Rick." My friends do.Thanks for your thoughts, and you are correct. Check out my Oct. 22 Reply to anamariatome.

## Re: A question regarding MATLAB's 'invfreqz()' command

Hi anamariatome.Thanks for pointing out that h(1) = NaN condition.(I hadn't noticed that.) To correct for that h(1) = NaN condition, I replaced my '[h,w] = freqz(b,...

## A question regarding MATLAB's 'invfreqz()' command

Hi. When I execute the following MATLAB code:   b = [1 0 0 0 -1]  a = [1, -1]  [h, w] = freqz(b, a, 64);  b_Order = length(b) -1; a_Order = length(a) -1;  ...

## Re: concept of bandwidth

Hi Sharan123.What, exactly, is your question?

## Re: CIC filter using prune width calculation

Hi singh2426v. You're welcome, and Good Luck with your CIC filter work.

## Re: CIC filter using prune width calculation

Hi.gretzteam is correct in his first Oct. 17th comment. At the end of my text accompanying my MATLAB code at:https://www.dsprelated.com/showcode/269.phpI wrote:"Warning:...

## Re: The first algorithm for computing the inverse chirp z-transform (ICZT) in O(n log n) time

Hi. That inverse chirp-z transform (ICZT) algorithm looks interesting, and I complement the Iowa State University professors for their clever work. However I can't...

## Re: Designing an IIR comb (peak) filter

Hi bobby_kI tried to run your code but it contains calls to functions 'tf()' and 'tfdata()" that I do not have.

## Re: Average Impulse Response from multiple measurements

Hi dudelsound. You are correct. And your words "the sweep starts at the same sample for all your measurements" are equivalent to my words "multiple time-domain signals...

## Re: Average Impulse Response from multiple measurements

Hello Samp17. I'm sure someone can answer your question is you would tell us, in detail, EXACTLY what you are doing. You wrote that you have "taken several log sine...

## Re: Efficient digital interpolation filter

Hello LC_Poon. You’re asking us to help explain why your computed numbers don’t agree with the computed numbers given in a paper that we cannot read. We don’t...

## Re: FFT Interpolation

Hi MrColly. You are most welcome.  You wrote, "the spectrum of a sine wave should be a Dirac delta function."That is theoretically true for a continuous (analog)...

## Re: FFT Interpolation

Hi MrColly. If you generated in Matlab an N-samaple sine wave sequence over exactly integer 'k' of cycles and performed an N-point DFT you would get a non-zero...

## Re: FFT Interpolation

Hi lamabrew. I like your notion of using the names sheep and goat domains.

...

## Re: FFT Interpolation

Hi. Here's my follow-up comment: In my earlier 'Reply' my phrase "true spectral magnitude of a finite-length sequence" is referring to the discrete-time Fourier...

## Re: FFT Interpolation

Hello MrColly. Your second paragraph contains two misconceptions. The first misconception is that an FFT assumes its input sequence repeats itself. Only a living...

## Re: Frequency estimation in between the bins ...

Hi. Slartibartfast gave you suggestions on finding more information about “fine” frequency estimation using FFT samples. To add to his list, you should also...

## Re: FIR filter shortening technique

Hello y MahmoodAburomoh.You ask a strange question. Tell us, why would you want to convert a 1024-tap FIR filter to a 3-tap FIR filter?

## Re: OFF TOPIC: A Question About PI

Hi bholzmayer.Thank you very much for your detailed June 28th "Reply." Number theory is indeed "The Queen of Mathematics."(And there's no need to warn me about possibly...

## Re: OFF TOPIC: A Question About PI

artmez, ya' know what's weird. The video link I posted contradicts the notion that the sum of all integers is -1/12, but Indian mathematician Srinivasa Ramanujan...

## Re: OFF TOPIC: A Question About PI

Hi artmez. Regarding the -1/12 notion, have you seen the analysis at:

## Re: OFF TOPIC: A Question About PI

Hi bholzmayer. I want to understand your 'First approach'. You wrote, "...look through pi (beginning from left, if you want) until you find a sequence which fits...

## OFF TOPIC: A Question About PI

Hi. Is the teacher in the following video correct in saying that every number is contained within the digits of pi?

## Re: Trying to create a virtual audio cable output from a software defined radio program

Hi iosman.Well, ...it's been three days since you post and you've received no replies. I believe that is so because of the vague terminology that you used in your...

## Re: Pool Ball Pendulum Animation in MATLAB

Hi djmaguire. Thanks for posting your code. Although the motions of the pool balls were noticeably "speeded up" in your mp4 video when played on my computer, your...

## Re: Pool Ball Pendulum Animation in MATLAB

Hi Cedron. I'm familiar with the ideas you presented. Your words correctly describe the purpose of the commands in my MATLAB code. To model the pendulums' motions,...

## Re: Pool Ball Pendulum Animation in MATLAB

Hi Jeff. I just saw your June 13th post five minutes ago.Your idea of a spectrograph is a good one! Thanks. I will explore that idea.

## Re: Filtering a white noise process in MATLAB to generate shadowing/fading?

Hi Shabaz.I share your uncertainty here. If you must pass a random-noise signal through a filter having a pole at z = exp(-d/20), and 'd' ranges from 0 -to- 200,...

## Re: Sign of the magnitude difference

Hi chalil.  Regarding your June 13th Reply, I think there's a missing 2 in your 4th line down, but your bottom line is correct. In any case I think the derivation...

## Re: Sign of the magnitude difference

Hi chalil. Can you give us more details on how you arrived at your Equation 2 (your equation for y squared)? Thanks.

## Re: Multistage decimation by two with halfband filters

Hello bertramaerts. You have NOT missed anything! You are correct and your uncertainty is my fault. And for this I beg your pardon. For an explanation please see...

## Re: Pool Ball Pendulum Animation in MATLAB

Hi jbrower. Watching the original pool ball pendulum video, it looked to me that the instantaneous East/West positions of the balls was VERY similar to the amplitudes...

## Re: Is this time-domain aliasing?

Hi friedman. Thanks for sharing that video with us!

## Re: Sign of the magnitude difference

Hi sudarshan_onkar. Your original post's question was interesting to me. Yesterday I didn't see any straightforward algebra solution to your problem, so I started...

## Re: Sign of the magnitude difference

Hi. To "follow-up" on my earlier June 10th post where I suggested rephrasing sudarshan's question to:"If I have the magnitude and phase of quantity z1-z2, is there...

## Pool Ball Pendulum Animation in MATLAB

Hi.Two weeks ago I posted a Forum message:https://www.dsprelated.com/thread/8675/is-this-tim...showing a video of oscillating pool ball pendulums. Because that Forum...

## Re: Sign of the magnitude difference

Hi sudarshan. I am confused by the words you used in your post. Three times you used the phrase "mag difference." If I replace your word "mag" with the word "number",...

## Re: Creating a real time map

Hi Rayonthetrack. You wrote: "Is this 2 bytes worth of data to be sampling real time?"What does your word "this" mean?Also, you wrote: "I am looking to log the activity...

## Is this time-domain aliasing?

Hi.I'm trying to figure out if the motion in this video is a physical embodiment of time-domain aliasing. (Watch the video for at least 60 seconds.)

## Re: Low cost audio DSP Exploration

Hi rtomkins. In an earlier reply you wrote: "I want to see this wonderful forum become a strong resource for others, people that are learning as well as people...

## Re: Low cost audio DSP Exploration

Hi rtomkins. I hope you do not abandon this web site. dsprelated.com is an educational and valuable web site for guys interested in DSP.

## Re: Spammers are getting more sophisticated

Good job Stephane!!

## Re: minimum phase HRTF reconstruction

Hi guzpomi.What are Earth do the acronyms "HRTF" and "ITD" mean?

## Re: Simulating higher order all-pass filters in matlab?

Hi szak1592. Good luck with your DSP studies on the MIT web site!

## Re: Simulating higher order all-pass filters in matlab?

Hi Dr. Mike. I hope all is well with you!

## Re: Simulating higher order all-pass filters in matlab?

Hi. In an earlier post of mine I wondered, "How do the MIT guys expect you to "Implement the filter for N=50"?" I can think of two ways to do that:[1] Compute the...

## Re: Simulating higher order all-pass filters in matlab?

Hi szak1592 (Shahbaz). I'm replying to your "At least there's something ..." post.[1] Here's my frequency response analysis of your original 'b' and 'a' coefficients:%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%...

## Re: Simulating higher order all-pass filters in matlab?

Hi szak1592 (Shahbaz). I am replying to your "It seems like I have figured..." post.Using your original 6th-order 'b' and 'a' allpass coefficients, when I tried...

## Re: Simulating higher order all-pass filters in matlab?

Hi szak1592 (Shahbaz). I'm replying to your "I am just attempting this DSP ..." post.I looked at page 3 of the MIT PDF file and, sure enough, MIT's Project I Part...

## Re: Simulating higher order all-pass filters in matlab?

Hi szak1592 (Shahbaz). I'm replying to your "I did the same before ..." post. If you run the code I listed in my above reply to kaz, and carefully compare the least-significant...

## Re: Simulating higher order all-pass filters in matlab?

Hi szak1592. Just out of curiosity, can you tell me what is the purpose of cascading 50 (fifty) 6th-order IIR allpass filters? Thanks. (I'm willing to bet one bottle...

## Re: Simulating higher order all-pass filters in matlab?

Hi kaz. Yes, you're right & I'm familiar with that 'tf2zp(b,a)' command. I wanted szak1592 to determine if his pole and zero magnitudes were EXACT reciprocals...

## Re: Simulating higher order all-pass filters in matlab?

Hi szak1592. Convolving your 'b' coefficients (raising the 'b' coeffs to the Nth power) and convolving your 'a' coefficients (raising the 'a' coeffs to the Nth power)...

## Re: What papers should beginners in signal processing research read?

Hi jimelectr. Ah but you did contribute to this topic! I enjoy hearing the opinions of working engineers regarding the literature of electrical engineering and signal...

## Re: Somewhat Off Topic: Manipulating a PDF File.

Hi rrlagic, djmaguire, ZaelixA (Achilles), bholzmayer, and weetabixharry. Thanks for all your suggestions. You guys rock!! I tried weetabixharry's link at: ...

## Somewhat Off Topic: Manipulating a PDF File.

Hi. I have a 30-megabyte PDF file containing a dozen, or so, signal processing papers. And I'd like to extract just the first paper in that large file and make the...

## Re: Timing Recovery Loop Filter Rate

Hi Dres. Like you, I am also fascinated by the clever DSP tricks I've encountered in the literature of DSP. And I've been "collecting" some of those tricks for the...

## Re: Timing Recovery Loop Filter Rate

Hi David.Thanks a lot for your detailed May 11th post. I can see that telephone signal processing is much more complicated than I had imagined!

## Re: Timing Recovery Loop Filter Rate

Hi dgshaw6.Under the assumption that you worked for AT&T at one time, I have a possibly dumb "telephone" question to ask of you. I have a simple ol' fashioned...

## Re: What papers should beginners in signal processing research read?

Hi szak1592.Asking me to recommend "readable" DSP articles is like asking me to recommend good Rock-n-Roll songs. It's all a "matter of opinion." And my opinion...

## Re: What papers should beginners in signal processing research read?

Hi szak1592.Well, ...we're not totally doomed. What we poor readers must typically do when plowing through a signal processing paper, as I wrote in the Preface of...

## Re: What papers should beginners in signal processing research read?

Hi szak1592. On the topic of general DSP there used to be two magazines that published, as you say, "papers that are easy to follow and also easy to reproduce...

## Re: Choosing the DFT size to match linear convolution in overlap save method?

Hi szak1592.Debugging DSP code certainly can be a pain in the neck.

## Re: Choosing the DFT size to match linear convolution in overlap save method?

Hi szak1592. I don't think your code is working properly. And I don't have time right now to examine your code in detail. But I do have a few suggestions for you....

## Re: “Improved” MZT/IIM type One pole LPF

Hi jtp_1960. If you define what your text "MZT/IIM" means, the subscribers here may have some idea what is the topic of your post.

## Re: Estimating SNR in the Frequency Domain

A  reply to ahmedshahein's 3/27/2019 message:Hi ahmedshahein. Three things: [1] As kaz said on 3/22/2019, "This issue is complicated." What I have learned is:...

## Re: Estimating SNR in the Frequency Domain

Hi ahmedshahein. OK, I'm back on duty. (It's early Saturday morning.) I experimented with your original 'statistics_32695.m' code. I see that you've updated...

## Re: Estimating SNR in the Frequency Domain

Hi ahmedshahein.I'll run your 'statistics_32695.m' file and see if I can be of any help to you.

## Re: What is the frequency response of a resampling filter?

Hi weetabixharry. I don't understand the spectral curves or the "timing offset" topic of your recent reply, but I can say you are correct in that your multirate...

## Re: Fixed point filter gain

dsplearn, how on Earth can anyone answer your question when you provided no information about for filters?

## Re: Filter a rectified waveform?

Hi steverak.Here's a diagram to support what omersayli wrote.The bold black voltage curve labeled "Waveform with capacitor" is the voltage labeled "+V" in the above...

## Re: questions of digital filter in a legacy application

HI John.My book has a bit more mathematics that Steven Smith's terrific book, but please know that I wrote my book to keep the mathematics at a low -to- moderate...

## Re: The Spectral Complexity of a Single Musical Note

Hi Cedron.Your referenced material, "The Hammer and the String" was very interesting. It clearly illustrates the complexity of what initially appears to be a simple...

## Re: The Spectral Complexity of a Single Musical Note

Hi Jeff. The article's title is "Automatic Music Transcription" which is the design of algorithms to convert audio music signals such as the following:                        ...

## The Spectral Complexity of a Single Musical Note

On page 25 of the most recent January issue of the IEEE Signal Processing Magazine the following interesting spectral plot was presented. That plot is the spectral...

## Re: Major Outage

"One who gains strength by overcoming obstacles possesses the only strength which can overcome adversity."               -Albert Schweitzer

## Re: Plotting panning law graph

Hi djmaguire.You are correct! Give that young man a kewpie doll.MATLAB's 'soundsc()' command will, indeed, play stereophonic audio.Thanks a lot!!

## Re: Plotting panning law graph

Hi. Here's the MATLAB code I used to plot the above curve in my earlier Feb. 16, 2019 post.% Filename: Stereophonic_panning.m%% Stereophonic panning example using...

## Re: Plotting panning law graph

Hi andresburgs.In you code, you should make a change so that as g2 increases in value, g1 must simultaneously decrease in value. We must ensure that g1 squared...

## Re: Plotting panning law graph

Hi andresburgs.Are you still working on your "panning law graphing" problem?By the way, this evening I developed a derivation for the following equation.

## Re: Plotting panning law graph

Hi Andresburgs.[1] I looked at the "ch5" material you referenced. The authors throw down the: equation and call it the "tangent law" with *NO* explanation of its...

## Re: Plotting panning law graph

Hi Andresburgs. Does MATLAB allow us to send two different signals to our left and right speakers? If so, I couldn't figure out how to do that. I also do not...

## Re: questions of digital filter in a legacy application

Hi John. Answer# 1: I prefer to write that equation as:   Trans. Reg. Width = 6.64*(Fs/2)/N Hz where the variable 'N' is dimensionless. When Fs = 256 Hz and...

## Re: questions of digital filter in a legacy application

Hi John.Answer# 1a): You wrote that "the source code states, transition bandwidth is 6.64FN/ N, where FN is the maximum system frequency and where N is the filter...

## Re: questions of digital filter in a legacy application

Hi John. I forgot to say, after the book arrives visit the following web page, scroll down to the "AMERICAN 3RD EDITION", and click on the words: "Errata 3rd Ed....

## Re: questions of digital filter in a legacy application

Hi John. If you have a copy of my "Understanding DSP" book. Start by reading Chapters 1 & 2, and then go to Chapter 5. Let me know if you have any questions...

## Re: questions of digital filter in a legacy application

Hi John. The above comment: "...where FN is the maximum system frequency..." is unfortunate because we don't know what the phrase "maximum system frequency" means.Also,...

## Re: questions of digital filter in a legacy application

Hi.To add just a little information to Laurent Millot's nice plots, below is your lowpass filter's frequency magnitude response plotted using a linear vertical axis....

## Re: questions of digital filter in a legacy application

Hello John1234567890.When designing a FIR filter using the "window method" the result of the design process is a sequence of numbers. That sequence of numbers is...

## Re: Modelling Squarewave Jitter with variable sample rate

Hi sudarshan_onkar.I am puzzled why your local oscillator is a square wave. It seems to me that the product of your incoming 20 MHz sinusoidal signal and a 20 MHz...

## Re: 50Hz and harmonics filtering

Hi dimaios.Would a filter whose freq magnitude response looks like the following:interest you? With an Fs = 1600 Hz sample, the filter has E = 8 notches in the positive...

## Re: Understanding the Comb Filter Frequency Response

Hi Luk_11. Your confusion is NOT your fault.The freq axis in the wikipedia spectral plot is incorrect. (Although I avoid such vulgarity, today's young people would...

## Re: Understanding the Comb Filter Frequency Response

Hi Luk_11. For u = 8 & g = 0.5, your network's frequency magnitude response (on a linear vertical axis and a freq axis that goes from minus half the sample...

## Re: Octave Frequency response of a filter - fft vs. freqz

Hi chab. In fact, right now, I'm trying to test a digital single-sideband (SSB) communications application that uses IIR Hilbert transformers. I'm performing two...

## Re: Octave Frequency response of a filter - fft vs. freqz

Hi chab. You are welcome.We can learn a useful lesson here. You were the victim of a situation I've experienced many times over the years. We have a digital system...

## Re: Octave Frequency response of a filter - fft vs. freqz

Hi chab.You didn't ask a specific question so I don't know what you're asking us. But I'll take a guess at what's bothering you.Your IIR filter is a super-narrowband...

## Re: Sampling frequency of slow phenomena to obtain PSDs

Hi alejo_latd. You know what is the answer to my question but you didn't tell me what is the answer to my question. The information you provided assumes I know...

## Re: Sampling frequency of slow phenomena to obtain PSDs

Hello alejo_latd. Regarding your spectral plot, what does it represent? In different words, that plot is the spectrum of what time-domain signal?

## Re: Phase Locked Loop Books in a time of DSP

Hello Y(J)S. Ah ha. I've seen that book's cover on the Internet before. Congratulations on having your book published.

Hi Brewster. Please send me a private e-mail at:R_dot_Lyons_@_ieee_dot_org.[-Rick-]

Hi lamabrew. When you refer to "Smith's book" are you referring to the material at:https://www.dsprelated.com/freebooks/sasp/Overlap_...It seems to me that the material...

## Re: Not understanding digital signal processing

Hi House_atr. If you want to learn DSP, if you have enthusiasm and don't give up, you will learn DSP. To quote Susan B. Anthony, "Failure is impossible." Send me...

Hi ctlee. It seems to me that if you want to reduce the peak-peak ripples in your filter's passband then you would window your filter's time-domain coefficients...

...

## Re: Not understanding digital signal processing

Hi Imoshe. Of my books, the book we're referring to here is described on the following web page:https://www.amazon.com/Understanding-Digital-Signa...

## Re: Phase Locked Loop Books in a time of DSP

Hello Y(J)S. What's the title of your book?

## Re: Not understanding digital signal processing

Hi House_atr.Your words didn't hurt my feelings, but rather they show me you are enthusiastic to learn more about DSP. You and I are kindred spirits. Thirty five...

## Re: Not understanding digital signal processing

Hello House_atr. I just now saw this Forum thread.My use of Eqs. (2-3) and (2-4) is my algebraic way of showing that Eq. (2-5) is equivalent to the last line of...

## Re: Understanding AD9364 Direct Conversion RFIC

Hi. Here's 'Part 2' of the article that brutor referenced:https://www.mwrf.com/active-components/differences...

## Re: How to efficiently control an FIR's magnitude response by altering its phase spectrum

Hi kaz. From fred's code, at the end of the 'k' loop (when k = 80) the frequency-domain behavior of the 64 complex-valued filter coefficients are shown below.

## Re: How to efficiently control an FIR's magnitude response by altering its phase spectrum

Hi fred.That's a neat demo routine! If just after yourH1=[0 H0(2:64).*exp(+1i*2*pi*0.0002*k*(-31:31).^2)]; command we insert the following six lines of code we'll...

## Re: Real to Complex conversion

Hello sachinwannabe.perhaps the information at the following web page will be of some value to you:https://www.dsprelated.com/showarticle/153.php

## Re: Gain Control

Hi Imoshe.Ah, I think you're trying to teach me a lesson. And you have succeeded.RMS = sqrt(mean(x.^2)) is only correct for real-valued signals. Your original...

## Re: Gain Control

Hi Imoshe.In the time domain it seems to me that the gain difference will be equal to the difference in the time-domain RMS values of the two signals.Also, just...

## Re: Gain Control

Hi Imoshe.You wrote, "how can I measure it correctly?". My question is, "Measure what?"Also, I wonder if you are using abs(x) to compute RMS values.

## Re: Gain Control

Whoa Imoshe, wait a minute! Let's use the proper terminology here. A single complex-valued FFT result sample has a real (imaginary) part that has an amplitude which...

## Re: Gain Control

[I posted this reply BEFORE I saw your above reply to kaz.]Hi Imoshe.If we use the variable x(n) to represent your 'Gain = 24 dB' signal, then your 'Gain = 30 dB'...

## Re: DSP Textbook Available Online

Hi wolf22. Yes, the "DSP Principles Algorithms and Applications" is NOT for beginners, that's for sure. Many professors use that book for their 1st-semester...

## Re: Octave BandPass Filter on Audio Wav Files

Even Nash, "Housewares", would recommend Smith's book.

## Re: Octave BandPass Filter on Audio Wav Files

Hi dingoegret. Yep, the "DSP Principles Algorithms and Applications" is NOT for beginners, that's for sure. Many professors use that book for their 1st-semester...

## Re: find out frequency of complex sinusoidal without FFT or DFT

Hi Mukul. Sorry for my clumsy typing.

## DSP Textbook Available Online

Purdue University's Prof. Michael Zoltowski is teaching a DSP class (ECE538 Digital Signal Processing I) using the 4th edition of the Proakis & Manolakis DSP...

## Re: find out frequency of complex sinusoidal without FFT or DFT

Hello mukel.Perhaps the following blog will be of some help to you. (Who knows?)https://www.dsprelated.com/showarticle/1045.php

## Re: Magnitude of "wav" files

Hi WFla. In the world of DSP, "amplitudes" can have positive or negative values. And "magnitudes" (the absolute value of an "amplitude") are positive values only....

## Re: Octave BandPass Filter on Audio Wav Files

Hello dingoegret. What DSP book did you buy?

## Re: PRISM - A new type of filter ?

Hi kaz. Thanks for the code. I'm going to experiment with it.

## Re: PRISM - A new type of filter ?

Hi woodpecker. Based on that "What is a Prism" web page it appears that "Prism Processing" is a technique for estimating the instantaneous frequency, instantaneous...

## Re: Off Topic: Binary Numbers

Hi woodpecker. Thanks for the interesting link. I saw that Leibniz' idea was used in Curta calculators. I'd like to have one of those calculators but they cost roughly...

## Re: Down sampling an iq signal

Hi tomb18.Ignoring any aliasing issues, let's say you have 1024 time-domain samples of a signal, you perform a 1024-pt FFT on those samples, and you see that some...

## Re: Windowing before FFT on packets of IQ datastream

Hello wa1x.If you're using FFTs to implement high-performance digital filtering, in a process called "fast convolution", then there is no need to window the time-domain...

## Re: Off Topic: Binary Numbers

Hi mukul.Of course I didn't read that long Pingala PDF file, but reading page 6 did not give me any clue that Pingala thought about representing decimal numbers...

## Re: Real to complex conversion in DSP (Hilbert Transform)

Hello mukul.Did you see the web page at:https://www.dsprelated.com/showarticle/153.php

## Off Topic: Binary Numbers

In a letter dated February 26, 1701, now in the collection of the French Academy of Sciences, German mathematician Gottfried Wilhelm Leibniz wrote the following...

## Re: Data overflow in fixed point DC removal filter, Richard Lyons Fig 13.65(b)

Hi Paul.I should make it clear here that I did not invent the filter in my book's Figure 13-65(b). Many years ago I first heard about that filter on the comp.dsp...

## Re: DC Blocking unexpected results

Hello Tony.Looking at the second image of your 8/19/2018 post, it looks to me like the DC blocking filter has reduced that spectral spike at zero Hz (DC) of the...

## Re: Data overflow in fixed point DC removal filter, Richard Lyons Fig 13.65(b)

Hi Paul. Referring to your 8/20/2018 post that starts with: "I decided to derive...", your idea of finding the "Y(z) divided by E(z)" error transfer function is...

## Re: Data overflow in fixed point DC removal filter, Richard Lyons Fig 13.65(b)

Hello Paul (I'm replying to your 8/20/2018 post that begins with the words: "To be more specific,..."). When I look at your nice image (qKJY8bowe4z.png) produced...

## Re: Data overflow in fixed point DC removal filter, Richard Lyons Fig 13.65(b)

Hello Paul.I've been checking my MATLAB code that modeled the filter in my Figure 13-65(b), and I could find to errors in that code, so far. However, thanks to you...

## Re: Data overflow in fixed point DC removal filter, Richard Lyons Fig 13.65(b)

Hi swirhun.I'm not ignoring you. I will go through my modeling software code for Figure 13-65(b) and see if I've made some sort of coding error. I'll get back to...

## Re: Removing DC Spike from an FFT

Hi Tom,you might want to try the following 45 coefficients in a delay-line FIR filter to implement a DC blocking filter:-0.001, -0.002, -0.003, -0.004, -0.006, -0.008,...

## Re: Removing DC Spike from an FFT

Hi Tom.Regarding your 'i' samples, if you computed the average of 16384 'i' samples (a single number) and subtracted that average value from each of the 'i' samples...

## Re: DC Blocking unexpected results

Hi Tony. Regarding the use of the words "amplitude" or "magnitude", what I wrote was correct. The vertical axis label of Figure 3 in the "Spectrum and spectral...

## Re: DC Blocking unexpected results

Hello Tony. I developed the "moving average" DC blocking filter based on real-valued (binary two's complement) input signals. But off the top of my head I see no...

## Re: High-cost communications in the old days -- telegrams

Hi Neil.Yes, in the ol' West the cost of a telegram was based on the number of transmitted letters in the message. That's why when Paladin (one of my boyhood TV...

## Re: A question on Rick Lyons' Understanding Digital Signal Processing 5.3.1 about Gibbs’s phenomenon

Hi Will. You asked an important question.As I stated in the text, we want 31 h(k) coefficients and we want them to be symmetrical in the time-domain. That is, we...

## Re: High-cost communications in the old days -- telegrams

Hi Neil.Thanks for the translation of "ASA." Like you, I don't understand most of the stunted, restricted, unexplained, infantile, cryptic, and confusing acronyms...

## Re: High-cost communications in the old days -- telegrams

Hi kaz.What does your word "socialize" mean?

## Far Off Topic: A Simple Geometry Problem That Had Me "Going in Circles"

At a garage sale recently I bought the book "More Marilyn, Some Like It Bright!" for one U.S. dollar. In that book the following simple geometry problem was posedThe...

## Re: DSP; Framing and Windowing in Audio Signal Processing

Hello sparrowjr.Someone here may be able to help you if you define (as clearly and completely as you are able) EXACTLY what your words: "make a new signal", "delay-line...

## Re: Problem implementing Sharpened CIC filters

Hi hirnprinz. I posted my original reply and then a minute or two later realized that the second part of my reply was incorrect. So I deleted the second part of...

## Re: Problem implementing Sharpened CIC filters

Hi hirnprinz. My congratulations to you on your very clearly written question.  The delay 'D' must be an integer when using the standard "Filter Sharpening" scheme...

## Re: Inverse filter

Hi Rahul. Sorry for my delayed reply. I haven't worked on any projects that required me to study deconvolution in any detail. After searching the web a little I...

## Re: Inverse filter

Hi Rahul. I think you want to perform what's called "deconvolution." And deconvolution can be performed (I) using your filter's output sequence (time-domain deconvolution)...

## Re: Need help - Pink noise analyzer

Hi FreeGameDev.Great. Please send a case of Sierra Nevada IPA to:Richard LyonsCell# 1638, Cell Block DFolsom State PrisonFolsom, California  95603

## Re: Does the reliability of band-pass filter output for a finite-time signal vary with frequency?

Hi achesir.If you apply an N-sample input sequence to a tapped-delay line FIR filter having 3N coefficients, your output sequence will have N+3N-1 = 4N-1 nonzero-valued...

...

## Re: Need help - Pink noise analyzer

Hi FreeGameDev.I went to the following web site:https://docs.unity3d.com/ScriptReference/AudioSour...I can't read the software gibberish on that page but I had the...

## Re: Direction finding with Uniform Circular Array

Hello Loganathan. I just encountered the following web site that may be of interest to you:https://cdn.everythingrf.com/live/direction-findin...

## Re: Need help - Pink noise analyzer

Hi. Regarding your question: "how I convert the fftResults to DB?", the answer is: For each complex-valued FFT output sample you must compute that sample's magnitude...

## Re: Does the reliability of band-pass filter output for a finite-time signal vary with frequency?

Hi.Slartibartfast is correct. Your use of the word "reliable" is puzzling. Does your word "reliable" mean "correct", or maybe "valid"?I'll stick my neck out here...

## Re: A Mathematical Notation Suggestion

What triggered my original post was the last sentence below (prior to the figure), from an article in the most recent issue of the IEEE Signal Processing Magazine...

## Re: A Mathematical Notation Suggestion

There's no need to discuss this topic with today's academics. Modern academics are the cause of this confusion in mathematical notation! How many classic papers...

## A Mathematical Notation Suggestion

At the risk of offending thousands of university professors, I have a suggestion for the IEEE journal/magazine Editors regarding signal processing manuscripts submitted...

## Re: Looking for Katja Vetter

Hi.  Ah, I see the address.  I'll use it to try to contact Ms. Vetter.  Thanks a lot Stephane!!

## Re: Looking for Katja Vetter

Hi Stenz. No I didn't, until just now. When I downloaded two of the Slice//Jockey .zip files, all I had were files that I couldn't open on my Windows System 7 computer....

...

## For those who downloaded the PDF file for Lyons' recent "FFT Interpolation" blog

Regarding my recent blog titled: "FFT Interpolation Based on FFT Samples: A Detective Story With a Surprise Ending", eagle-eye DerekB detecting a missing minus sign...

## Re: Zero Lag Filter

Hi John. Can you post the coefficients of your filter (the filter having poles & zeros) here?  I'd like to "plug" those coefficients into my filter-analysis...

## Re: CIC Filter "zero-crossing" Distortion

Hi JingCI tried to run your MATLAB code but the following command requires an undefined variable 'T':[x sd] = sd_mod(FS, 1e-3/0.021, F0, T);What is the missing command...

## Re: DSP diagramming software?

I use Microsoft VISIO.  I patronize Microsoft because Bill Gates needs the money.

## Re: Graphical or mathematical depiction of asymmetric spectrum of complex baseband signal around 0 Hz.

Hello chiwang_shum.  Thank you for your kind words. I appreciate them.Your idea of plotting 3-dimensional spectra is a good idea. However, the image you posted...

## Re: Graphical or mathematical depiction of asymmetric spectrum of complex baseband signal around 0 Hz.

Hello chiwang_shum.  Here's the answer to your question. Open a new web browser page, go to the following web page, look at Figure 1, and then return here to read...

## Re: z-transform: Confused on how to find ROC of H(z)

Hi DSPer1. With regard to Regions of Convergence, you might find the following blog to be interesting:https://www.dsprelated.com/showarticle/993.php

## Re: DSP History

Hi Neil. Your interesting post makes me recall similar memories. In EE undergraduate school at the University of Akron (in the early 70's) the first half of one...

## Re: DSP History

Hi Steve. I understand exactly what you talking about. The clear, thorough but not overly-complicated, conceptual approach is so very obvious in your "Scientist...

## Re: DSP History

Hi Steve.  Ah ha.  That explains a lot!  Thomas Stockham was one of the most productive and famous of the early DSP Algorithm Kings.

## DSP History

For those of you interested in the history of DSP, you might find the following article noteworthy:Oppenheim-2012-Algorithm-Kings.pdf

## Re: Book Review of Paul Nahin's "An Imaginary Tale: The Story of √-1"

Hi Coop. Regarding Heaviside, I agree with you and I believe he deserves to be at least as famous as, say, Brad Pitt or George Clooney. To appreciate Heaviside's...

## Book Review of Paul Nahin's "An Imaginary Tale: The Story of √-1"

For those of you who enjoyed reading the book "An Imaginary Tale: The Story of √-1", by Paul Nahin, here's a very interesting and revealing book review by Brian...

## Square waves

I thought I fully understood the notion of square waves. Not so!  Here are real square waves. (Photo taken off the coast of the French island Isle of Rhe.)

...

## Re: Lyons needs help with a "Frequency Estimation" paper.

Hi John.  You're reminding me that someday I should study the MUSIC frequency estimation process.

## Lyons needs help with a "Frequency Estimation" paper.

Hi Troops.I'm unable to understand a paper describing what the authors' call a "new frequency estimation algorithm."  For those of you who have plenty of free time...

## Re: Inversion properties of Convolution / Deconvolution

Hi nelsona."Wet" and "dry" huh?  Interesting!  (Sadly, I don't speak the lingo of audio signal processing.) Do you have the word "damp"?  As is in, "That damp...

## Re: Inversion properties of Convolution / Deconvolution

Hi nelsona.  I see that your questions were posted two days ago but no one has attempted to reply to you. I think that's because you questions are difficult to...

## Re: Real-time Wavelet Transform

Hi Nehavedam.  Eric Jacobsen and I have asked you to give us more details regarding the kind of FIR filtering you need (desire).  But you haven't given us those...

## Re: Real-time Wavelet Transform

Hi Nehavedam.  In your original post you wrote that your signal "needs to be filtered in real time."  Perhaps it would help if you descried your desired filtering...

## Re: Looking for tips to improve SNR

Greg, Uh oh!  I wonder if you are performing AM demodulation properly. Are you performing something equivalent to the scheme in Figure 4 at: https://www.dsprelated.com/showarticle/938.phpto...

## Re: Looking for tips to improve SNR

So Greg, looking at the spectral drawing I posted on Jan. 24th, is your goal to detect the presence of the 511 Hz (or the 1489 Hz) tone? Stated in different words,...

## Re: Looking for tips to improve SNR

Hi Greg. I'm not able to understand the analog processing as you describe it in your 2nd paragraph. Can you tell me, if your original input analog carrier signal...

## Re: Looking for tips to improve SNR

Hi GregLapin. I agree with fred harris. It's easier for people to give you useful suggestions if you post a block diagram of your receiver, and sprinkle your diagram...

## Re: Side lobes reduction after FFT

Hi fred.As always, your paper is very interesting and the figures therein are simply terrific! In case anyone's interested, an alternate description of that time-folding...

## Re: Impulse behavior of FIR LP filter

Hi Bernhard.  Are you able to post an image here of the time-domain samples contained in your input "pulse"?

## Re: Artifacts in Time Varying IIR Filters

Hi dszabo. I am the Editor of, and a contributor to, that "Streamlining DSP" book.  It's a collection of articles, by many authors, that appeared in the "DSP Tips...

## Re: Artifacts in Time Varying IIR Filters

Hi dszabo.My my.  You've received some high-powered advice!  Both Fred harris and Steve Smith are holders of "Black Belts" in the field of DSP.

## Re: How to downconvert a Complex RF signal in Matlab?

Hi.  I'm sure the guys here can answer all your questions, but they need more information from you M_313.  Are you able to post a block diagram here of your digital...

## Re: Off Topic: A geometry problem

Hi Ced.  I'm sure you and I both understand this geometry problem and that we're actually in "agreement".  Did you see my most recent post down at the bottom of...

## Re: Off Topic: A geometry problem

Hi Ced.   On a 2-dimensional plane, you seem to be saying that the locations of the following two points, C and C', are equal to each other.  I think the locations...

## Re: Off Topic: A geometry problem

Hi Guys.   Thanks for all your replies.It just hit me!!  In the book's solution, the first sentence should have been: "Draw a line, called "m", through the row...

## Re: Off Topic: A geometry problem

Hi.  If we move line m, the book's solution will produce a new location for point C.  (In the book's solution, point C must always lie on line m.)

## Re: Off Topic: A geometry problem

Hi bholzmayer.  If you're interested in my solution, just scroll down in this thread.

## Re: Off Topic: A geometry problem

Hi dsplib.  I agree with you.  If you're interested in my solution, just scroll down in this thread.

## Re: Off Topic: A geometry problem

Hi.  If you're interested in my solution, just scroll down in this thread.

## Re: Off Topic: A geometry problem

Hi Steve.  I was happy to read that Example 6 also bothered you.  If you're interested in my solution, just scroll down in this thread.

## Re: Off Topic: A geometry problem

Hi. I believe (1)this problem is a minimization problem, and (2)there is only one correct answer for the location of point C. The book's solution to finding point...

## Re: Off Topic: A geometry problem

Hi.  Are you saying there is more than one correct answer to this minimization problem?

## Re: Off Topic: A geometry problem

Hi Kaz. The problem's question is clearly stated.  Unless I'm missing something here, there is one, and only one, correct answer for the location of point C. If...

## Re: Off Topic: A geometry problem

Hi Greg.  In my opinion, the only thing wrong with the geometry book's given solution is that it is incorrect.  If you're interested in my solution, just scroll...

## Off Topic: A geometry problem

Hi Troops.  Forgive me for posting a non-DSP topic here, but I simply had to show the following to someone. I was looking at my grandson' high school "Common Core"...

## Re: What is Windowing and when/why do we need it?

Hi Steve.   Nice to hear from you.[-Rick-]

## Re: AGC on FPGA

Hi Neil.  I've never seen that web page before!  I see that the "Embedded" web site folks deleted the references I provided in that section of my DSP book.  Most...

I have an account on the LinkedIn.com web site. Some months ago I exchanged a half dozen e-mails with a businessman in my town. Let's call him "Joe Jones."  A few...

## Re: An Oddball Electrical Engineering Question

Hi JohnEhlers.  You're not disagreeing, you're informing. Thanks for the information.

## Re: An Oddball Electrical Engineering Question

Hi Guys.  Thanks for all your replies!

## An Oddball Electrical Engineering Question

I've been trying to learn about satellite antennas. And in my studies, unexpected ideas have occurred to me. For example, I just realized that the flashlight ("torch"...

## Re: complex exponential - what Am I missing?

Sharan123, don't worry.  The only people who never makes mistakes are people who never do anything.  :-)

...

## Re: Removing frequency components and reconstruct time domain signal.

Hi. I initially had the same question as mukul.  Your statement, "I don't want to use any bandpass filter because it only attenuates the frequencies outside the...

## Re: How to measure voltage and power of the B200 device using oscilloscope?

Hi cogwsn.  Nice photo!!

## Re: Magnitude/phase vs real/imaginary

There most certainly are plots of complex-valued sequences.  But as kaz said, such plots must be in three dimensions.  Such a plot can be found as the blue curve...

## Re: Need Help In Interpreting Curves in a Chart

dszabo, jbrower, and Chris Felton, thanks for your thoughts regarding my questions!

## Re: FFT Speed, FIR Output

Hi.  The mathematics of the Figure 2 envelope detector that I referred to is very simple.  But you do need to know: (i) what is a lowpass digital filter, (ii)...

## Re: FFT Speed, FIR Output

Roger, matched filters, Goertzel, FFTs, envelope detectors, etc., Sheece!  People are making all sorts of suggestions to you based on what they think you're trying...

## Re: DTFT of a signal

Hi Sharan123.   kaz's May 13 reply made me realize my brain was not working when I posted my above reply.  No explicit summation command in software is needed...

## Re: Need Help In Interpreting Curves in a Chart

Hi Chris.  So you're saying the y-axis in Figure 5 is simply time (seconds). OK. I'll buy that.  Yes, I saw the authors' words that "the computational complexity...

## Re: FFT Speed, FIR Output

Hello groger. I'm assuming you have a digital signal sequence comprising noise-only samples and then suddenly the signal is a 100 Hz (or 150 Hz) sinusoid for roughly...

## Need Help In Interpreting Curves in a Chart

In the most recent edition of the IEEE Sig. Proc. Magazine was an article discussing a new technique to perform sample rate change (SRC) [1]. The authors started...

## Re: DTFT of a signal

Hi Sharan123.  Keep in mind, the DTFT is an equation and the 'w' (omega) frequency variable in that equation is continuous. We cannot use or "compute" continuous...

## Re: Matlab code for SSB demodulation using phasing method

Hello Daniel.  I just saw your post this morning. Have you solved your 'MATLAB SSB demodulation' problem?

Hi.  You're using some sort of high-powered software to design your filter.  Be aware that the software will design a filter it thinks you "want" rather than the...

## Re: DSP Filter Verification in FPGA

Hello srid.  Perhaps the material at the following web page will be of some small value to you:https://www.dsprelated.com/showcode/269.php

## Re: DFT of a signal and system

Hi.  Just to add my 'two cents': A discrete sequence has a DFT (a discrete spectrum). A system (such as a digital filter, differentiator, Hilbert transformer, etc.)...

## Re: Subharmonic distortion?

Hello dszabo.  Good for you NOT ignoring an anomaly that you could have just as well ignored. I wonder, does the unwanted 500 Hz spectral component appear at different...

## Re: sum of sinusoids

Hello Sharan123.  You above post is messed up.  Your plots' window seems to be covering up some part of your post.  In any case, I suggest you set variable L1...

## Re: sum of sinusoids

Sharan123, if you have MATLAB then try this code:  n = 0:128;  for K = -2:0.25:2;    x = 1*sin(2*pi*n*16/128) + 10^K*sin(2*pi*n*14/128);     figure(1), clf   ...

## Re: sum of sinusoids

To Sharan123: Your original signal plots are correct, but you added two sine waves (differing in frequency by one Hz) whose frequencies are low relative to the Fs...

## Re: sum of sinusoids

Hi dszabo. Or perhaps it would be more correct to say, "The addition of two sinusoids, having different frequencies, is mathematically equivalent to a third sinusoid...

## Re: sum of sinusoids

Hi. When you add two sinusoids of frequencies f1 and f2 you produce a third sinusoid whose frequency is (f1 + f2)/2.  And that third sinusoid's peak amplitude is...

## Re: Multi-Impulse Response Deconvolution

Hi.  What does it mean to "convolve a signal with two impulse responses"? Is the result of such a process one output sequence or two separate output sequences?

## Re: How to work out the dynamic range of a filter empiracally

Hi andrewstanfordjason. Your question has very deep and subtle implications. That's because multirate (decimation) filters do not have a frequency response in the...

## Re: Deriving FIR coefficients for a higher sample rate

Hi probbie, I'm tickled the scheme I posted works for you. Thanks for the beer.  If you'd like I'll send you the errata for your copy of my book.  All you have...

## Re: Deriving FIR coefficients for a higher sample rate

Hi David, thanks for the kind words.  The notion of using a polyphase FIR interpolation process never occurred to me! There see, ...that's why they pay you the...

## Re: Deriving FIR coefficients for a higher sample rate

Hello David.  I've not heard of your scheme before.  It sounds very interesting and I'm gonna experiment using it. Thanks for posting your scheme!

## Re: How to calculate time delay estimation?

nateduong, you wrote:  "I want to make sure I did right or wrong?"I suggest you create your own very simple "transmit" and "receive" signal sequences and apply...

## Re: Deriving FIR coefficients for a higher sample rate

Hi.  I wonder if the following "time-domain interpolation-by-M using frequency-domain zero stuffing" scheme will work for you [h(n) are your original FIR coefficients]:•...

## Re: Difference b/w array 3dB beam width and array bearing resolution

Hi. At first I thought your text "b/w" stood for "bandwidth" but it turns out it means "between."  naumankalia, correct spelling makes it easier for people to read...

## Re: Odd Convolution Results

Hello nelsona. I bet someone here can help you, but you'll have to help us do that by providing more information. What the mathematical nature of this thing you...

## Re: Noise removing

Hi. Regarding AM demodulation, perhaps the following blog would be of some interest to you:https://www.dsprelated.com/showarticle/938.php

## Re: The adoption of the frequency measure "Hertz"

Neil, your keen sense of humor put the following look on my face:

## The adoption of the frequency measure "Hertz"

Digging through some old papers, I found the following on a page that I tore out of the November 1965 Hewlett-Packard Journal:

## Re: Need to understand: How noise is folded into BW of interest after LP filtering+decimatiom

Hi. I suggest that you do not, if possible, use a squarewave as a test signal. Squarewaves are NOT bandlimited so any discrete signal representation of a squarewave...

## Re: Complex envelope and analytic signals.

Hi.  Somewhat unfortunately in MATLAB, using the command 'y = hilbert(x);' does NOT produce 'y' sequence that is the real-valued Hilbert transform of the real-valued...

## Re: Need to understand: How noise is folded into BW of interest after LP filtering+decimatiom

Hi. To see how spectral energy folds when CIC decimation filters are used, see Figure 6 at:http://www.embedded.com/design/configurable-system...Your method of estimating...

## Re: Complex envelope and analytic signals.

Lucky_12, in your MATLAB code did you intend to write:    f_c = 11.725e9 Our did you intend to write:    f_c = 11.75e9   (Note the '.75' versus the...

## Re: measure signal power

Hi.  kaz's March 4th comment told you how to measure the frequency behavior of your filter. You can verify the results of kaz's test by comparing the spectral magnitude...

## Re: measure signal power

Hi.  There are two types of "power" that we talk about regarding discrete sequence: (i) the "instantaneous power", and the (ii) "N-point average power".The instantaneous...

## Re: Generalized Cross Correlation method not producing desired results

Hi. Do you have a question for the people here?

## Re: Interpolation and power

mkm10, to experience a sense of personal satisfaction it's better for you to answer your question yourself--either by drawing time-domain sequences on paper or by...

## Re: Interpolation and power

Hi.  spetcavitch is correct.  Try this:Generate a low-frequency sine wave sequence whose peak amplitude is one.  Upsample that sequence by four, by inserting...

## Re: Filter design

Sharan123, you wrote:    "So, given f1, f2, Fs, we are computing N values      for Fs = 19200 or 384000?"Your words are not in the form of a question but...

## Re: Adjustment of window length with sliding/moving RMS method for frequency drifts

johnny_smith911, referencing your post that begins with "Yes, I think ...":I can't interpret your two curves' time relationship because you did not label their horizontal...

## Re: Filter design

Sharan123, referencing your post that begins with "I am still trying ...":Let's change that equation to the product of two ratios, as:    N = (Fs/delta_f) * (Atten(dB)/22).Looking...

## Re: Adjustment of window length with sliding/moving RMS method for frequency drifts

Thanks Stephane!![-Rick-]

## Re: Adjustment of window length with sliding/moving RMS method for frequency drifts

johnny_smith911, it seems to me that you are performing the following:where the above x(n) input sequence is your squared input samples, my 'D" is your 'N', and...

## Re: Adjustment of window length with sliding/moving RMS method for frequency drifts

Hi Stephane,   That is EXACTLY what I entered into the editor, except I only had one '$' at the beginning and one '$' at the end of the line of my MathJax characters....

## Re: Filter design

Sharan123, you wrote:   "Case 1: f1 = 10000; f2 = 15000; Fs = 192000    Case 2: f1 = 10000; f2 = 15000; Fs = 384000    My design parameter remain the same...

## Re: Adjustment of window length with sliding/moving RMS method for frequency drifts

Hi johnny_smith911. I spent 15 minutes trying to enter two MathJax equation in a reply for you, but I failed.  So I deleted my first reply and now I will try again...

## Re: Filter design

Sharan123, please clarify you question, OK?

## Re: Filter design

Sharan123, whoa, wait!  You wrote, "...if Fs was very high then N too would be high,...".  What you should have written is, "...if the ratio of Fs/delta_f was...

## Re: Filter design

Sharan123, the code you posted does two things: (1) it uses an empirical formula to compute a rough estimate, N, of how many coefficients (taps) are needed by a...

## Re: Interpolation and filter gain

In the traditional method of interpolation by integer K, by inserting (K-1) samples in between each original input sample, there is an output amplitude loss by a...

## Re: Amplitude calculation from cross correlation data

Hi Amartansh.  I think charansal is pointing you in the correct direction, and kaz's warning is sensible. It seems to me that you should explore the topic of "deconvolution." ...

## Re: Digital filter

If you search the Internet for:   free digital filter designyou should see a number of free filter design software programs that you can download and start experimenting...

## Re: harmonic distortion of a single-tone excitation

I believe the answer to your first question is Yes. Let's assume your Phi1 = p and w1 = 2*pi*f1. If your input is:    x(t) = A1*sin(w1*t + p), the output...

## Re: Complexity of DSP magazine articles - Opinions requested

Hi Mike.  The article I referred to was 10.5 pages in length.

## Complexity of DSP magazine articles - Opinions requested

The IEEE Signal Processing Magazine has a monthly column titled: "Lecture Notes". Those Lecture Notes articles are intended to be "easily accessible, being proper...

## Re: Spurious when Fs/F is not an integer

Hello Loganathan N.  In your original post, the notion of "frequency resolution" makes no sense regarding a digital to analog converter. That's why I was confused....

## Re: Spurious when Fs/F is not an integer

Hi.  I have two questions:[1] What is the definition of "frequency resolution" with regard to a digital to analog converter.[2] Are you able to post your MATLAB...

## Re: 'Phase drift' if oscillator doesn't go through full 360 deg rotation when mixing FIR to bandpass

Kevin,   Frerking's book is out of print.  I'll scan my copy of that book's appropriate pages for you.  Send me a private e-mail at:R_dot_Lyons_@_ieee_dot_org.I'm...

## Re: 'Phase drift' if oscillator doesn't go through full 360 deg rotation when mixing FIR to bandpass

Hi Kevin,Regarding the text you quoted in your original post,   "In general the signal(s) of interest are not at baseband, ...",can you tell from where that quote...

## Re: 'Phase drift' if oscillator doesn't go through full 360 deg rotation when mixing FIR to bandpass

Hi Kevin,I was thinking of scanning the few pages from my copy of Frerking's  book that discuss this topic, and sending you that material.  But I was lucky. ...

## Re: 'Phase drift' if oscillator doesn't go through full 360 deg rotation when mixing FIR to bandpass

Hi,Please forgive my sloppy nomenclature.  You are correct, my words "tap" and "coefficient" mean the same thing. And yes, you'll need to store 21*21=441 coefficients...

## Re: 'Phase drift' if oscillator doesn't go through full 360 deg rotation when mixing FIR to bandpass

Hi. There is a way to perform frequency translation and FIR filtering simultaneously.  The scheme only works if the translation frequency is an integer submultiple...

## Re: ARM CMSIS FFT - does it produce correct results?

Hi.  Try these tests: Test# 1: Fill your input buffer with 512 samples with each sample having an amplitude of +1. Your magnitude spectrum should show energy...

## Re: down conversion vs de-modulation

Sharan123. After you implement frequency translation, by way of multiplication by a real-valued sinusoid or a complex-valued complex exponential, I hope you are...

## Re: Envelope Detection

Hello martinvicanek. In my limited software experimentation with these various envelope detectors I noticed that different detectors appeared to perform better than...

## Re: down conversion vs de-modulation

Hi Sharan123.  Your confusion is understandable. In the literature of signal processing some authors use the phrase "demodulation" when they should more correctly...

## Re: Understanding maths behind DFT?

Hi Dhaval, the DFT is the single most important topic in DSP. So learn all you are able regarding the DFT. (For your work, keep in mind that the DFT is used to determine...

## Re: Matlab Home-use version

barcelonajack, ha ha.  Matlab focuses on large data sets. Kardashians focus on large sets.

## Re: Matlab Home-use version

Hi barcelonajack,  What kind of software tool is a Kardashian?

## Re: Matlab Home-use version

Hi Neil.   You are correct.  I "bit the bullet" and purchased the MATLAB "Home" version last week. I also bought the 'Signal Processing Toolbox' and the 'DSP...

## Re: Understanding maths behind DFT?

Hello Dhaval. I do not understand the question you asked in the last paragraph of your post.  Can you clarify your question using different words?

## Re: Understanding maths behind DFT?

Hello dhaval_shah,The following web page may be helpful to you. The comments on that web page were written by guys who at one time were in exactly the same situation...

## Re: Understanding maths behind DFT?

Hi AllenDowney. Your comment invites meditation. In one way I agree with you. I don't know how the Parks-McClellan FIR filter design algorithm works. Yet I've used...

## Re: Understanding maths behind DFT?

Hi fred3, if you have an Americanversion of the of my "Understanding DSP" book I can send you the appropriate errata for your copy of my book if you can tell me...

## Re: Downsampling from 2.0 MHz to 192kHz

Hi tomb18. If I understand your wishes correctly, what you want to do is "resample" both of your 2-MHz I & Q signals by a factor of 12/125. (My verb "resample"...

## Re: Downsampling from 2.0 MHz to 192kHz

Hi tomb18. You have a quadrature (I/Q) at a sample rate of 2 MHz. Such a signal has an information-carrying bandwidth of 2 MHz. (A critical question: Is that I/Q...

## Re: Downsampling from 2.0 MHz to 192kHz

Hi Mike. I like your suggestion because its involves small numbers. Do you mean "go up by 3, then down by 5 then up by 2 then down by 5 twice"?[-Rick-]

## Re: A New Reverse IIR Filtering Algorithm

Hello Martin. I'd like to understand the details of your filtering scheme. (Looking briefly at your block diagrams, your scheme is reminiscent of a cascaded integrator-comb...

## Re: Power Measurement of Complex Signal

Hi b2508,   There are MANY signal processing concepts for you to keep in mind here.[1] An analog sinusoidal waveform has four voltage characteristics; its average...

## Re: Zero-Padding as scalloping loss attenuator

Hi jmarcelold, I didn't say anything about mixed-radix FFTs. I said "five individual 256-point FFTs."  In any case, perhaps the material in the following blog...

## Re: Zero-Padding as scalloping loss attenuator

Dear Mike, Ha ha. You have more confidence in me than I do. Regretfully, my memory is just about as reliable as the paper towel dispenser in the Men's Room.

## Re: Zero-Padding as scalloping loss attenuator

Hello jmarcelold, My understanding of the DFT characteristic called “scalloping” is described in the following blog. https://www.dsprelated.com/showarticle/538.php...

## Re: Power Measurement of Complex Signal

Hello b2508. Your original question is worded in a strange way. You made statements there that we cannot fully understand. We can read your words but we don't know...

## Re: Decimate by M and Interpolate by L interchangeable if L and M are relatively prime

This looks like homework problem 4.7 on page 179 of Vaidyanathan's DSP book. My limited math skills prevent me from solving this problem, but I did have the following...

## Re: SSB Demodulation

Hi.   When you wrote "SSB Demodulation that I found online says that ..." it would be nice for us to know exactly which online SSB website you're referring to....

## Re: Invert Phase Response

Hello Kaz,   Will you give us more details on what you have in mind? Thanks.

## Re: Invert Phase Response

jtp_1960, Please forgive me. I made a mistake in my first Reply. When coefficients: den = [4.86512631333559, 1.915296632059649, -2.86512631333559]num = [16.38734500433902,...

## Re: Invert Phase Response

Hi jtp_1960,  In my MATLAB modeling of your *first* set of feedforward and feedback coefficients, I obtained the same magnitude and phase plots as you provided...

## Re: CIC Filter

Hi Chris.  Thanks![-Rick-]

## Re: CIC Filter

Hello dkgupta,You wrote "(2*2)^2= 8" and you meant to write, "(2*2)^2= 16".In an earlier post you wrote "(10*2)^5" and I said that surprised me. Thinking about it...

## Re: CIC Filter

Hi dkgupta, You wrote: “In my case the gain is (10*2)^5…” That surprised me. I haven’t experimented with CIC filters when the differential delay = 2.Does...

## Re: CIC Filter

Hi spetcavich, Thanks for posting that web link address. That link is useful because fred harris’s book is ‘Out of Print’.

## Re: CIC Filter

Hi. The gain of a 5th-order CIC decimation filter is D^5, and individual integrators within the filter can experience overflow. (An integrator’s gain is infinite...

## Re: Window-presum FFT problem

n2ic,Dr. Mike's August 16 reply is a good one.  I hope it made sense to you.Regarding your "precisely the problem" reply, it seems to me that your value for N must...

## Re: Best Real Time Convolution Algorithm?

Hi,I bet someone here will help you if you can more clearly describe what you want.  Your terminology is puzzling.  What, exactly, is a "window kernel"?  What's...

## Re: Window-presum FFT problem

Hi, The first sentence of your second paragraph really puzzles me. I'll assume that what you mean is that you're trying to reduce the leakage in the results of...

## Re: How to estimate the SNR

Hi Chess,From what you wrote, you have r = Ac+n and you want to estimate SNR = (Power of c)/(Power of n), or perhaps SNR = (Power of Ac)/(Power of n). But A, c,...

## Re: Error Growth for Various Goertzel Resonators

Hi Aaron45,It looks like you've done a lot of work to compile all those tables. And your results may well be both instructive and useful. The problem is, it's too...

## Re: PLL in presence of noise

Chess, Y(j)S makes a good point. As it turns out, there are digital differentiators that don't generate too much high-freq noise and their performance is pretty...

## Re: Polyphase CIC structure

flutekick, your question is not very specific. I'm not sure what you mean by "pointers."The traditional notion of "decimation filtering" is to lowpass filter a signal...

## Re: Adding 45 degrees phase shift to a FIR bandpass

Dear Wolfgang, Your English grammar is VERY good! I do not understand everything you wrote in your last reply. I have too many questions to ask of you and I...

## Re: Adding 45 degrees phase shift to a FIR bandpass

Dear wolf22, I'm not sure that I can be of help because I'm not sure what you are trying to do. If I recall correctly, you want to perform single-sideband (SSB)...

## Re: Adding 45 degrees phase shift to a FIR bandpass

Herr wolf,  I wonder if the material at:www.faculty.ece.vt.edu/swe/argus/iqbal.pdfwould be of some use to you.Tschuss,[-Rick-]

## Re: Zero IF vs Low IF receivers

Hello tomb18,  Perhaps the pdf file at:http://www.cs.tut.fi/kurssit/TLT-5806/RecArch.pdfmay be of some use to you.

## Re: fft combinations

Hi Kaz,I can assure you, there are NO missing steps in the diagram I presented. The 1st step "unzips" the 2N-sample real-valued a(n) input sequence to generate an...

## Re: fft combinations

Hello Kaz,Yes, there's a way to compute a 512-point FFT (on real-valued input samples) using a standard complex-valued 256-point FFT software algorithm. I cover...

## Re: Sound Pressure Level Measurement using a digital Mic

Perhaps the material at:https://en.wikipedia.org/wiki/Sound_pressurewill be of some help to you.

## Re: A digital filter question

Hi Neil, to elaborate on my "fall into the trap" comment:For example, if your 'b' coefficients are [1,1,1,1] then H_B(z) has zeros at: -1, +j, and -j on the z-plane....

## Re: A digital filter question

Hi Mike. I'm guessing that you're implementing something like the following:where the 'Delay' is equal to the group delay of your H_B(z) moving average filter.

## Re: A digital filter question

Hi wtmission, is there any chance you could paste the diagram you have in mind (from Chapter 2) here in a future 'reply'?  I'd sure be tickled to see it. (If it's...

## Re: A digital filter question

Hi Neil,It's easy to fall into the trap of thinking that the zeros (poles) of H_B(z) become the poles (zeros) of the H_A(z) filter. But that's not true as you have...

## Re: A digital filter question

Hello Shahram, by "digital implementation" I mean: computing the y(n) output sequence, from the following filter, given the x(n) input sequence.

## Re: A digital filter question

Hello Jerry,I can easily believe that the above process might be used in the analog world.  But my question was about a digital implementation.PS. If you are the...

## A digital filter question

I have a vague memory of sometime in the past encountering a digital filter block diagram like the following accompanied by text stating something like:[1] If H_B(z)...

## Re: Restorative Upsampling

Hi Boyboy,After modifying the MATLAB-illegal commands (including the illegal   'w2c = conj((fliplr(w2b'))');'command) I as was able to run your code. Your code...

## Re: Restorative Upsampling

Boyboy, in MATLAB the following x = 1 2 3 4 5is called a "row vector" because it has one row and multiple columns. And in MATLAB the following x = 12345is called...

## Re: Restorative Upsampling

Boyboy, I sense a possible "learning moment" here.I'm trying to figure out EXACTLY what your code does. To do that I need to replace your illegal commands with legal...

## Re: Restorative Upsampling

Hello Boyboy,Your post piqued my interest. I have two questions:[1] With regard to a signal, can you give us a precise definition for your word "Bandlimit"?[2] In...

## Re: Does decimation of a signal result in a shift in the baseline noise?

Hi, I've been a away from my computer for a few days.tomb18, I'm confused. If your had 16384 samples of the 2-Msps signal then after decimation you should only have...

## Re: Pass band in digital up conversion of LTE signals

LabPe43,How can we explain the signal processing described in a Xilinx article if you didn't give us a web link so we can read the article?

## Re: Does decimation of a signal result in a shift in the baseline noise?

tomb18, the answer to your post’s title question finally “hit” me. And the answer is “In spectral plots, yes, decimation results in an increase in the average...

## Re: Does decimation of a signal result in a shift in the baseline noise?

tomb18,I agree with Prof. Smith (JOS). The average signal-to-noise ratio (SNR) of your decimated signal should be equal to the average SNR of your original input...

## Re: Phase rotation after matched filtering

Hi mkm10,  You'll have a better chance of receiving a meaningful answer to your question if you can give us more details of the signal processing you have in mind....

## Re: FDATool

LabPe43, to answer your last question, if freq-domain filtering is what you desire then the first step is to merely compute the FFT of the 'h' coefficients as: ...

## Re: FDATool

To echo Dr. mike's good advice: if your FDAtool produces filter coefficients, h, whose performance is what you desire, then you should use the h coefficients filter...

## Re: Newbie with questions about decimation for SDR

tomb18, thanks for the pointer to the SDRPlay hardware!!

## Re: Newbie with questions about decimation for SDR

Hi tomb18.  I said "we'll figure this out", and I meant it.  Is there a way I can download your original 2.048-MHz sample rate file in the 'xxx.wav' format? (That...

## Re: Newbie with questions about decimation for SDR

tomb18, the positive-frequency cutoff frequency of your lowpass filter should be just less than +128 kHz. If you pass your original input signal through your...

## Re: Newbie with questions about decimation for SDR

tomb18, looking at your ‘2msps-with-filter.jpg’ spectrum, if you’re decimating by 8 it appears to me that your lowpass filter’s passband is too wide. For...

## Re: Newbie with questions about decimation for SDR

Ah ha tomb18. You’re making things exciting for us by NOT labeling the horizontal axes of your spectra in Hz. Now we have to guess, “Where is zero Hz on the...

## Re: Newbie with questions about decimation for SDR

tomb18, don’t worry. We’ll figure this all out. First, do not multiply anything by a window sequence, such as a Blackman window. We’ll worry about windowing...

## Re: Newbie with questions about decimation for SDR

A simple, and efficient, solution to decimation by 8 is to perform three separate stages of decimation by 2. And in each decimation by 2 stage use a half-band FIR...

## Re: Decimator Image response

Hello neirober. Your post is thought provoking. [1] I'm not familiar with the phrase "image response." Is there a formal definition for the phrase "image response"?...

## Re: 90 Degrees Shift of Digital Signal

Hello TheCyrus. The blog that dhad referred to can be found at:https://www.dsprelated.com/showarticle/153.phpAnother blog that may be of some interest to you can...

## Re: How is calculated the "effective alias sidelobe supression" of a Decimation Filter?

Hello jluqueq, My compliments to you on the very sensible variable names in your MATLAB code. They made it easy for me to read your code. Based on my estimates...

## Re: Implement 2nd order IIR filter

Hi,  You're most welcome.  If you wish, let us know how things work out for you.

## Re: Implement 2nd order IIR filter

Dimitar,   One thing you can do is called "filter scaling." From my DSP textbook, if the passband gain of your IIR filter is GIIR then you can reduce that gain...

## Re: IIR non-causal Wiener filter solution giving unstable filter

Hi Ruskywow,   I don't work with Weiner filters (pronounced as "veener", not "weener.") But I did try to repeat your polynomial algebra. Here are my results:As...

## Re: How is calculated the "effective alias sidelobe supression" of a Decimation Filter?

Hello jluqueq, Like you, I am unable to answer your sensible question. You probably already wrote down these numbers but I'll mention them anyway: 20*log(1/64)...

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