Evaluate Noise Performance of Discrete-Time Differentiators

Neil Robertson March 28, 20225 comments

When it comes to noise, all differentiators are not created equal.  Figure 1 shows the magnitude response of two differentiators.  They both have a useful bandwidth of a little less than π/8 radians (based on maximum magnitude response error of 2%).  Suppose we apply a signal with Gaussian noise to each of these differentiators.  The sinusoidal signal with noise is shown in the top of Figure 2.  Signal frequency is π/12.5 radians.  The output of the so-called...


Off-Topic: A Fluidic Model of the Universe

Cedron Dawg February 2, 20223 comments
Introduction

This article is a followup to my previous article "Off Topic: Refraction in a Varying Medium"[1]. Many of the concepts should be quite familiar and of interest to the readership of this site. In the "Speculations" section of my previous article, I mention the goal of finding a similar differential equation as (18) of [1] for light traveling in gravity. It turns out it is the right equation, but a wrong understanding. As a consequence of trying to solve this puzzle, a new...


Learn About Transmission Lines Using a Discrete-Time Model

Neil Robertson January 12, 2022

We don’t often think about signal transmission lines, but we use them every day.  Familiar examples are coaxial cable, Ethernet cable, and Universal Serial Bus (USB).  Like it or not, high-speed clock and signal traces on printed-circuit boards are also transmission lines.

While modeling transmission lines is in general a complex undertaking, it is surprisingly simple to model a lossless, uniform line with resistive terminations by using a discrete-time approach.  A...


Determination of the transfer function of passive networks with MATLAB Functions

Josef Hoffmann December 7, 20212 comments

With MATLAB functions, the transfer function of passive networks can be determined relatively easily. The method is explained using the example of a passive low-pass filter of the sixth order, which is shown in Fig.1

Fig.1 Passive low-pass filter of the sixth order

If one tried, as would be logical, to calculate the transfer function starting from the input, it would be quite complicated. On the other hand, if you start from the output, the determination of this function is simple...


A DSP Quiz Question

Rick Lyons December 5, 202112 comments

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...

The Discrete Fourier Transform and the Need for Window Functions

Neil Robertson November 15, 20212 comments

The Discrete Fourier Transform (DFT) is used to find the frequency spectrum of a discrete-time signal.  A computationally efficient version called the Fast Fourier Transform (FFT) is normally used to calculate the DFT.  But, as many have found to their dismay, the FFT, when used alone, usually does not provide an accurate spectrum.  The reason is a phenomenon called spectral leakage.

Spectral leakage can be reduced drastically by using a window function in conjunction...


The 2021 DSP Online Conference

Stephane Boucher September 29, 20212 comments

The 2021 DSP Online Conference is just around the corner and this year again, the program is packed with opportunities for DSP engineers to refresh their DSP skills and learn a few new tricks along the way. 

By registering for the conference, not only will you have full access to all talks, workshops, and Q&A sessions at this year's event, but you'll also gain instant access to all talks from last year's...


Modeling Anti-Alias Filters

Neil Robertson September 26, 2021

Digitizing a signal using an Analog to Digital Converter (ADC) usually requires an anti-alias filter, as shown in Figure 1a.  In this post, we’ll develop models of lowpass Butterworth and Chebyshev anti-alias filters, and compute the time domain and frequency domain output of the ADC for an example input signal.  We’ll also model aliasing of Gaussian noise.  I hope the examples make the textbook explanations of aliasing seem a little more real.  Of course, modeling of...


In Search of The Fourth Wave

Allen Downey September 25, 20212 comments

Last year I participated in the first DSP Related online conference, where I presented a short talk called "In Search of The Fourth Wave". It's based on a small mystery I encountered when I was working on Think DSP.  As you might know:

 A sawtooth wave contains harmonics at integer multiples of the fundamental frequency, and their amplitudes drop off in proportion to 1/f.  A square wave contains only odd multiples of the fundamental, but they also drop off...

Sampling bandpass signals

Josef Hoffmann June 26, 20215 comments
Sampling bandpass signals 1.1 Introduction

It is known [1], [3] that bandpass signals can be sampled with a sampling frequency which is lower than the sampling frequency according to the sampling theorem.

Fig. 1 shows an example of how the spectrum of a bandpass signal sampled with $f_s$ (Fig. 1a) arises in the baseband with $−f_s / 2 ≤ f < f_s/2$. The bandpass signal is assumed to have a center frequency $f_c = (f_{max} + f_{min})/2$ and bandwidth $\Delta f...


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

Rick Lyons April 3, 201620 comments

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)...


Design IIR Butterworth Filters Using 12 Lines of Code

Neil Robertson December 10, 201712 comments

While there are plenty of canned functions to design Butterworth IIR filters [1], it’s instructive and not that complicated to design them from scratch.  You can do it in 12 lines of Matlab code.  In this article, we’ll create a Matlab function butter_synth.m to design lowpass Butterworth filters of any order.  Here is an example function call for a 5th order filter:

N= 5 % Filter order fc= 10; % Hz cutoff freq fs= 100; % Hz sample freq [b,a]=...

Handling Spectral Inversion in Baseband Processing

Eric Jacobsen February 11, 20089 comments

The problem of "spectral inversion" comes up fairly frequently in the context of signal processing for communication systems. In short, "spectral inversion" is the reversal of the orientation of the signal bandwidth with respect to the carrier frequency. Rick Lyons' article on "Spectral Flipping" at http://www.dsprelated.com/showarticle/37.php discusses methods of handling the inversion (as shown in Figure 1a and 1b) at the signal center frequency. Since most communication systems process...


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

Rick Lyons 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:

$$ Forward \ FFT \rightarrow X(m) = \sum_{n=0}^{N-1} x(n)e^{-j2\pi nm/N} \tag{1} $$ $$ Inverse \ FFT \rightarrow x(n) = {1 \over N} \sum_{m=0}^{N-1}...

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

Rick Lyons March 26, 202048 comments

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...


Use Matlab Function pwelch to Find Power Spectral Density – or Do It Yourself

Neil Robertson January 13, 201938 comments

In my last post, we saw that finding the spectrum of a signal requires several steps beyond computing the discrete Fourier transform (DFT)[1].  These include windowing the signal, taking the magnitude-squared of the DFT, and computing the vector of frequencies.  The Matlab function pwelch [2] performs all these steps, and it also has the option to use DFT averaging to compute the so-called Welch power spectral density estimate [3,4].

In this article, I’ll present some...


The DFT Magnitude of a Real-valued Cosine Sequence

Rick Lyons June 17, 201410 comments

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...


Python scipy.signal IIR Filtering: An Example

Christopher Felton May 19, 2013
Introduction

In the last posts I reviewed how to use the Python scipy.signal package to design digital infinite impulse response (IIR) filters, specifically, using the iirdesign function (IIR design I and IIR design II ).  In this post I am going to conclude the IIR filter design review with an example.

Previous posts:


Understanding and Relating Eb/No, SNR, and other Power Efficiency Metrics

Eric Jacobsen May 29, 20123 comments

Introduction

Evaluating the performance of communication systems, and wireless systems in particular, usually involves quantifying some performance metric as a function of Signal-to-Noise-Ratio (SNR) or some similar measurement. Many systems require performance evaluation in multipath channels, some in Doppler conditions and other impairments related to mobility. Some have interference metrics to measure against, but nearly all include noise power as an impairment. Not all systems are...


Free DSP Books on the Internet

Rick Lyons February 23, 200824 comments

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...


Sensors Expo - Trip Report & My Best Video Yet!

Stephane Boucher August 3, 20183 comments

This was my first time at Sensors Expo and my second time in Silicon Valley and I must say I had a great time.  

Before I share with you what I find to be, by far, my best 'highlights' video yet for a conference/trade show, let me try to entertain you with a few anecdotes from this trip.  If you are not interested by my stories or maybe don't have the extra minutes needed to read them, please feel free to skip to the end of this blog post to watch the...


Who else is going to Sensors Expo in San Jose? Looking for roommate(s)!

Stephane Boucher May 29, 20186 comments

This will be my first time attending this show and I must say that I am excited. I am bringing with me my cameras and other video equipment with the intention to capture as much footage as possible and produce a (hopefully) fun to watch 'highlights' video. I will also try to film as many demos as possible and share them with you.

I enjoy going to shows like this one as it gives me the opportunity to get out of my home-office (from where I manage and run the *Related sites) and actually...


Crowdfunding Articles?

Stephane Boucher April 12, 201828 comments

Many of you have the knowledge and talent to write technical articles that would benefit the EE community.  What is missing for most of you though, and very understandably so, is the time and motivation to do it.   

But what if you could make some money to compensate for your time spent on writing the article(s)?  Would some of you find the motivation and make the time?

I am thinking of implementing a system/mechanism that would allow the EE community to...


Embedded World 2018 - More Videos!

Stephane Boucher March 27, 20181 comment

After the interview videos last week, this week I am very happy to release two more videos taken at Embedded World 2018 and that I am proud of.  

For both videos, I made extensive use of my two new toys, a Zhiyun Crane Gimbal and a Sony a6300 camera.

The use of a gimbal like the Zhiyun makes a big difference in terms of making the footage look much more stable and cinematographic.

As for the Sony camera, it takes fantastic slow-motion footage and...


Embedded World 2018 - The Interviews

Stephane Boucher March 21, 2018

Once again this year, I had the chance to go to Embedded World in Nuremberg Germany.  And once again this year, I brought my video equipment to try and capture some of the most interesting things at the show.  

Something new this year, I asked Jacob Beningo if he would partner with me in doing interviews with a few vendors.  I would operate the camera while Jacob would ask the right questions to the vendors to make them talk about the key products/features that...


Finally got a drone!

Stephane Boucher August 28, 20172 comments

As a reader of my blog, you already know that I have been making videos lately and thoroughly enjoying the process.  When I was in Germany early this summer (and went 280 km/h in a porsche!) to produce SEGGER's 25th anniversary video, the company bought a drone so we could get an aerial shot of the party (at about the 1:35 mark in this video).  Since then, I have been obsessing on buying a drone for myself and finally made the move a few weeks ago - I acquired a used DJI...


SEGGER's 25th Anniversary Video

Stephane Boucher July 18, 20172 comments

Chances are you will find this video more interesting to watch if you take five minutes to first read the story of the week I spent at SEGGER's headquarters at the end of June.  

The video is only a little more than 2 minutes long.  If you decide to watch it, make sure to go full screen and I would really love to read your thoughts about it in the comments down bellow.  Do you think a video like this succeeds in making the viewer want to learn more about the company?...


Went 280km/h (174mph) in a Porsche Panamera in Germany!

Stephane Boucher July 10, 201712 comments

Those of you who've been following my blog lately already know that I am going through some sort of mid-life crisis that involves going out there to meet people and make videos.  It all started with Embedded World early this year, then continued at ESC Boston a couple of months ago and the latest chapter just concluded as I returned from Germany after spending a week at SEGGER's headquarters to produce a video to highlight their 25th anniversary.  


Going back to Germany!

Stephane Boucher June 13, 20176 comments

A couple of blog posts ago, I wrote that the decision to go to ESC Boston ended up being a great one for many different reasons.  I came back from the conference energized and really happy that I went.  

These feelings were amplified a few days after my return when I received an email from Rolf Segger, the founder of SEGGER Microcontroller (check out their very new website), asking if I would be interested in visiting their headquarters...