A Simpler Goertzel Algorithm
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...
Find Aliased ADC or DAC Harmonics (with animation)
When a sinewave is applied to a data converter (ADC or DAC), device nonlinearities produce harmonics. If a harmonic frequency is greater than the Nyquist frequency, the harmonic appears as an alias. In this case, it is not at once obvious if a given spur is a harmonic, and if so, its order. In this article, we’ll present Matlab code to simulate the data converter nonlinearities and find the harmonic alias frequencies. Note that Analog Devices has an online tool for...
Adaptive Beamforming is like Squeezing a Water Balloon
Adaptive beamforming was first developed in the 1960s for radar and sonar applications. The main idea is that signals can be captured using multiple sensors and the sensor outputs can be combined to enhance the signals propagating from specific directions and attenuate (null out) signals from other directions. It has grown immensely in recent years as processors have become faster and cheaper. Today, adaptive beamforming applications include smart speakers (like the Amazon Echo),...
Compute Images/Aliases of CIC Interpolators/Decimators
Cascade-Integrator-Comb (CIC) filters are efficient fixed-point interpolators or decimators. For these filters, all coefficients are equal to 1, and there are no multipliers. They are typically used when a large change in sample rate is needed. This article provides two very simple Matlab functions that can be used to compute the spectral images of CIC interpolators and the aliases of CIC decimators.
1. CIC InterpolatorsFigure 1 shows three interpolate-by-M...
Exploring Human Hearing Range
Human Hearing RangeIn this post, I'll look at an interesting aspect of Audacity – using it to explore the threshold of human hearing. In my book Digital Signal Processing: A Gentle Introduction with Audio Examples, I go into this topic and I include a side note on the amazing hearing range of our canine companions.
Creating a Test Audio FileAudacity allows for the generation of a variety of test signals. If you click the Generate->Tone menu, it looks something like...
The DSP Online Conference - Right Around the Corner!
It is Sunday night as I write this blog post with a few days to go before the virtual doors of the very first DSP Online Conference open..
It all started with a post in the DSPRelated forum about three months ago. We had just had a blast running the 2020 Embedded Online Conference and we thought it could be fun to organize a smaller event dedicated to the DSP community. So my goal with the post in the forum was to see if...
The Zeroing Sine Family of Window Functions
IntroductionThis is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by introducing a class of well behaved window functions that the author believes to be previously unrecognized. The definition and some characteristics are displayed. The heavy math will come in later articles. This is an introduction to the family, and a very special member of it.
This is one of my longer articles. The bulk of the material is in the front half. The...
Design Square-Root Nyquist Filters
In his book on multirate signal processing, harris presents a nifty technique for designing square-root Nyquist FIR filters with good stopband attenuation [1]. In this post, I describe the method and provide a Matlab function for designing the filters. You can find a Matlab function by harris for designing the filters at [2].
BackgroundSingle-carrier modulation, such as QAM, uses filters to limit the bandwidth of the signal. Figure 1 shows a simplified QAM system block...
Make Hardware Great Again
By now you're aware of the collective angst in the US about 5G. Why is the US not a leader in 5G ? Could that also happen -- indeed, is it happening -- in AI ? If we lead in other areas, why not 5G ? What makes it so hard ?
This hand-wringing has reached the highest levels in US government. Recently the Wall Street Journal reported on a DoJ promoted plan 1 to help Cisco buy Ericsson or Nokia, to give the US a leg up in 5G. This is not a new plan,...
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,...
Free DSP Books on the Internet
While surfing the "net" I have occasionally encountered signal processing books whose chapters could be downloaded to my computer. I started keeping a list of those books and, over the years, that list has grown to over forty books. Perhaps the list will be of interest to you.
Please know, all of the listed books are copyrighted. The copyright holders have graciously provided their books free of charge for downloading for individual use, but multiple copies must not be made or printed. As...
Filtering Noise: The Basics (Part 1)
IntroductionFinding signals in the presence of noise is one of the fundamental quests of the discipline of signal processing. Noise is inherently random by nature, so a probability oriented approach is needed to develop a mathematical framework for filtering (i.e. removing/suppressing) noise. This framework or discipline, formally referred to as stochastic signal processing, is often taught in graduate level engineering programs and is covered from different perspectives in excellent...
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 DesignerWith typical filter design software packages the user enters numerical values for the...
Digital PLL's -- Part 2
In Part 1, we found the time response of a 2nd order PLL with a proportional + integral (lead-lag) loop filter. Now let’s look at this PLL in the Z-domain [1, 2]. We will find that the response is characterized by a loop natural frequency ωn and damping coefficient ζ.
Having a Z-domain model of the DPLL will allow us to do three things:
Compute the values of loop filter proportional gain KL and integrator gain KI that give the desired loop natural...Adventures in Signal Processing with Python
Author’s note: This article was originally called Adventures in Signal Processing with Python (MATLAB? We don’t need no stinkin' MATLAB!) — the allusion to The Treasure of the Sierra Madre has been removed, in deference to being a good neighbor to The MathWorks. While I don’t make it a secret of my dislike of many aspects of MATLAB — which I mention later in this article — I do hope they can improve their software and reduce the price. Please note this...
IIR Bandpass Filters Using Cascaded Biquads
In an earlier post [1], we implemented lowpass IIR filters using a cascade of second-order IIR filters, or biquads.
This post provides a Matlab function to do the same for Butterworth bandpass IIR filters. Compared to conventional implementations, bandpass filters based on biquads are less sensitive to coefficient quantization [2]. This becomes important when designing narrowband filters.
A biquad section block diagram using the Direct Form II structure [3,4] is...
Linear-phase DC Removal Filter
This blog describes several DC removal networks that might be of interest to the dsprelated.com readers.
Back in August 2007 there was a thread on the comp.dsp newsgroup concerning the process of removing the DC (zero Hz) component from a time-domain sequence [1]. Discussed in that thread was the notion of removing a signal's DC bias by subtracting the signal's moving average from that signal, as shown in Figure 1(a).
Figure 1.
At first I thought...
The Number 9, Not So Magic After All
This blog is not about signal processing. Rather, it discusses an interesting topic in number theory, the magic of the number 9. As such, this blog is for people who are charmed by the behavior and properties of numbers.
For decades I've thought the number 9 had tricky, almost magical, qualities. Many people feel the same way. I have a book on number theory, whose chapter 8 is titled "Digits — and the Magic of 9", that discusses all sorts of interesting mathematical characteristics of the...
The DFT Magnitude of a Real-valued Cosine Sequence
This blog may seem a bit trivial to some readers here but, then again, it might be of some value to DSP beginners. It presents a mathematical proof of what is the magnitude of an N-point discrete Fourier transform (DFT) when the DFT's input is a real-valued sinusoidal sequence.
To be specific, if we perform an N-point DFT on N real-valued time-domain samples of a discrete cosine wave, having exactly integer k cycles over N time samples, the peak magnitude of the cosine wave's...
Round Round Get Around: Why Fixed-Point Right-Shifts Are Just Fine
Today’s topic is rounding in embedded systems, or more specifically, why you don’t need to worry about it in many cases.
One of the issues faced in computer arithmetic is that exact arithmetic requires an ever-increasing bit length to avoid overflow. Adding or subtracting two 16-bit integers produces a 17-bit result; multiplying two 16-bit integers produces a 32-bit result. In fixed-point arithmetic we typically multiply and shift right; for example, if we wanted to multiply some...
Generating pink noise
In one of his most famous columns for Scientific American, Martin Gardner wrote about pink noise and its relation to fractal music. The article was based on a 1978 paper by Voss and Clarke, which presents, among other things, a simple algorithm for generating pink noise, also known as 1/f noise.
The fundamental idea of the algorithm is to add up several sequences of uniform random numbers that get updated at different rates. The first source gets updated at...
Interpolation Basics
This article covers interpolation basics, and provides a numerical example of interpolation of a time signal. Figure 1 illustrates what we mean by interpolation. The top plot shows a continuous time signal, and the middle plot shows a sampled version with sample time Ts. The goal of interpolation is to increase the sample rate such that the new (interpolated) sample values are close to the values of the continuous signal at the sample times [1]. For example, if...
Frequency Dependence in Free Space Propagation
Introduction
It seems to be fairly common knowledge, even among practicing professionals, that the efficiency of propagation of wireless signals is frequency dependent. Generally it is believed that lower frequencies are desirable since pathloss effects will be less than they would be at higher frequencies. As evidence of this, the Friis Transmission Equation[i] is often cited, the general form of which is usually written as:
Pr = Pt Gt Gr ( λ / 4πd )2 (1)
where the...
Embedded Toolbox: Programmer's Calculator
Like any craftsman, I have accumulated quite a few tools during my embedded software development career. Some of them proved to me more useful than others. And these generally useful tools ended up in my Embedded Toolbox. In this blog, I'd like to share some of my tools with you. Today, I'd like to start with my cross-platform Programmer's Calculator called QCalc.
I'm sure that you already have your favorite calculator online or on your smartphone. But can your calculator accept...
Linear-phase DC Removal Filter
This blog describes several DC removal networks that might be of interest to the dsprelated.com readers.
Back in August 2007 there was a thread on the comp.dsp newsgroup concerning the process of removing the DC (zero Hz) component from a time-domain sequence [1]. Discussed in that thread was the notion of removing a signal's DC bias by subtracting the signal's moving average from that signal, as shown in Figure 1(a).
Figure 1.
At first I thought...
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.
...The Number 9, Not So Magic After All
This blog is not about signal processing. Rather, it discusses an interesting topic in number theory, the magic of the number 9. As such, this blog is for people who are charmed by the behavior and properties of numbers.
For decades I've thought the number 9 had tricky, almost magical, qualities. Many people feel the same way. I have a book on number theory, whose chapter 8 is titled "Digits — and the Magic of 9", that discusses all sorts of interesting mathematical characteristics of the...
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 ReviewFigure 2(a) depicts the process of decimation by an integer factor D. That...
A Differentiator With a Difference
Some time ago I was studying various digital differentiating networks, i.e., networks that approximate the process of taking the derivative of a discrete time-domain sequence. By "studying" I mean that I was experimenting with various differentiating filter coefficients, and I discovered a computationally-efficient digital differentiator. A differentiator that, for low fequency signals, has the power of George Foreman's right hand! Before I describe this differentiator, let's review a few...
Code Snippets Suggestions
Despite being only a couple of months old, the Code Snippet section ( DSPRelated.com/code.php ) already contains tens of snippets, thanks to the contributors who have taken the time to share their code.
But let's not stop here - there is room for several hundreds more snippets before the database can be said to cover a decent portion of the DSP field.
To keep the momentum going, I will do two things:
First, I am modifying the rewards program. Instead of...
Latest DSP Books
As you may already know, Rick Lyons has just published a new edition of his highly acclaimed book: "Understanding Digital Signal Processing". This book has been getting very high ratings and positive reviews from the DSP community since the publication of the first edition. The 3rd edition seems to contain more than enough new material to justify replacing your old copy.
Also of possible interest to you, a new DSP book by C. Britton Rorabaugh titled "
Code Snippets Section Now LIVE
The new code sharing section is now live and can be accessed HERE.
Please take a few minutes to rate and/or comment the snippets that you have the expertise to judge.
If you think of some code snippets that you would like to share with the DSP community, please apply to become a contributor HERE.
If you are not aware of the reward program for contributors, your can learn about it HERE.
As always, your comments and suggestions are...
New Code Sharing Section & Reward Program for Contributors!
UPDATE (11/02/2010): The code section is now live.
UPDATE 2 (01/31/2011): The reward program has changed. A flat fee of $20 per code snippet submitted will now be paid.
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I am very happy to finally announce the imminent launch of the new code sharing section. My vision for this new section is a rich library of high quality code snippets for the DSP community, from processor specific functions to Matlab or Scilab routines, from the simplest filter...
50,000th Member Announced!
In my last post, I wrote that DSPRelated.com was about to reach the 50,000 members mark. Well, I am very happy to announce that it happened during the holidays, and the lucky person is Charlie Tsai from Taiwan. Charlie is an assistant professor in the Department of Electrical Engineering at the National Central University in Taiwan where he teaches the "Biomedical Signal Processing" class. He is also the advisor of the
Almost 50,000 Members!
I am very happy to announce that DSPRelated.com will reach the 50,000 registered members mark before the end of 2009. To celebrate this milestone, I will buy a BMW 5 to the 50,000th person to register (please make sure to confirm you email address to activate your registration). Please read the fine prints after the picture.
I am just having fun here and it's not even April's fool day. The 50,000th member won't get a BMW (I wish I could offer it!),...
DSPRelated faster than ever!
if you are visiting DSPRelated.com on a regular basis, you should observe that the site loads significantly faster in your browser than it used to, especially if you are in Europe or in Asia. The main reason for this is that I am now using Amazon's CloudFront service for the delivery of most static content on DSPRelated.com (images, javascripts, css). The cloudFront service automatically detects the location of a visitor and will deliver the static content from the server...
New Papers / Theses Section
The new 'Papers & Theses' section is now online: http://www.dsprelated.com/documents.phpThe idea is to list and organize in one place as many DSP related dissertations (PhD & Masters) and papers/articles as possible.If you are the author of a thesis or paper and would like to have it listed on DSPRelated.com, please follow these steps:- Make sure that you are allowed to share the document online (copyright).- If you don't already have one, make a 'pdf' copy of your document. ...
New Blog Section!
By now, chances are you have noticed the new blogs section (you are actually in it right now!).
Following an email I sent to the members of the site, a few weeks ago, asking for dsp engineers willing to blog here, I received around 50 propositions. I have selected an initial set of 10 bloggers (that I will soon introduce into a seperate post) and I am currently in the process of creating their accounts. Markus and Parth have already...
New Discussion Group: DSP & FPGA
I have just created a new discussion group for engineers implementing DSP functions on FPGAs. The creation of this group has been on my todo list for a long time. If you want to join the group, send a blank email to: fpgadsp-subscribe@yahoogroups.com
As usual, it should take a few weeks before there are enough members for interesting discussions to get started.