Take Control of Noise with Spectral Averaging

Sam Shearman April 20, 20183 comments

Most engineers have seen the moment-to-moment fluctuations that are common with instantaneous measurements of a supposedly steady spectrum. You can see these fluctuations in magnitude and phase for each frequency bin of your spectrogram. Although major variations are certainly reason for concern, recall that we don’t live in an ideal, noise-free world. After verifying the integrity of your measurement setup by checking connections, sensors, wiring, and the like, you might conclude that the...

Linear Feedback Shift Registers for the Uninitiated, Part XIV: Gold Codes

Jason Sachs April 18, 2018

Last time we looked at some techniques using LFSR output for system identification, making use of the peculiar autocorrelation properties of pseudorandom bit sequences (PRBS) derived from an LFSR.

This time we’re going to jump back to the field of communications, to look at an invention called Gold codes and why a single maximum-length PRBS isn’t enough to save the world using spread-spectrum technology. We have to cover two little side discussions before we can get into Gold...

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

Rick Lyons April 16, 201840 comments

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.


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

ADC Clock Jitter Model, Part 1 – Deterministic Jitter

Neil Robertson April 16, 201817 comments

Analog to digital converters (ADC’s) have several imperfections that affect communications signals, including thermal noise, differential nonlinearity, and sample clock jitter [1, 2].  As shown in Figure 1, the ADC has a sample/hold function that is clocked by a sample clock.  Jitter on the sample clock causes the sampling instants to vary from the ideal sample time.  This transfers the jitter from the sample clock to the input signal.

In this article, I present a Matlab...

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...

How precise is my measurement?

Sam Shearman March 28, 20183 comments

Some might argue that measurement is a blend of skepticism and faith. While time constraints might make you lean toward faith, some healthy engineering skepticism should bring you back to statistics. This article reviews some practical statistics that can help you satisfy one common question posed by skeptical engineers: “How precise is my measurement?” As we’ll see, by understanding how to answer it, you gain a degree of control over your measurement time.

An accurate, precise...

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...

Phase or Frequency Shifter Using a Hilbert Transformer

Neil Robertson March 25, 201821 comments

In this article, we’ll describe how to use a Hilbert transformer to make a phase shifter or frequency shifter.  In either case, the input is a real signal and the output is a real signal.  We’ll use some simple Matlab code to simulate these systems.  After that, we’ll go into a little more detail on Hilbert transformer theory and design. 

Phase Shifter

A conceptual diagram of a phase shifter is shown in Figure 1, where the bold lines indicate complex...

Feedback Controllers - Making Hardware with Firmware. Part 8. Control Loop Test-bed

Steve Maslen March 21, 2018

This part in the series will consider the signals, measurements, analyses and configurations for testing high-speed low-latency feedback loops and their controllers. Along with basic test signals, a versatile IFFT signal generation scheme will be discussed and implemented. A simple controller under test will be constructed to demonstrate the analysis principles in preparation for the design and evaluation of specific controllers and closed-loop applications.

Additional design...

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...

Recruiting New Bloggers!

Stephane Boucher October 16, 20157 comments

Previous calls for bloggers have been very successful in recruiting some great communicators - Rick LyonsJason Sachs, Victor Yurkovsky, Mike Silva, Markus NentwigGene BrenimanStephen Friederichs,

Why Time-Domain Zero Stuffing Produces Multiple Frequency-Domain Spectral Images

Rick Lyons March 23, 20154 comments

This blog explains why, in the process of time-domain interpolation (sample rate increase), zero stuffing a time sequence with zero-valued samples produces an increased-length time sequence whose spectrum contains replications of the original time sequence's spectrum.


The traditional way to interpolate (sample rate increase) an x(n) time domain sequence is shown in Figure 1.

Figure 1

The '↑ L' operation in Figure 1 means to...

Spline interpolation

Markus Nentwig May 11, 20147 comments

A cookbook recipe for segmented y=f(x) 3rd-order polynomial interpolation based on arbitrary input data. Includes Octave/Matlab design script and Verilog implementation example. Keywords: Spline, interpolation, function modeling, fixed point approximation, data fitting, Matlab, RTL, Verilog


Splines describe a smooth function with a small number of parameters. They are well-known for example from vector drawing programs, or to define a "natural" movement path through given...

Discrete Wavelet Transform Filter Bank Implementation (part 1)

David October 27, 20101 comment

UPDATE: Added graphs and code to explain the frequency division of the branches

The focus of this article is to briefly explain an implementation of this transform and several filter bank forms. Theoretical information about DWT can be found elsewhere.

First of all, a 'quick and dirty' simplified explanation of the differences between DFT and DWT:

The DWT (Discrete Wavelet Transform), simply put, is an operation that receives a signal as an input (a vector of data) and...

A Simple Complex Down-conversion Scheme

Rick Lyons January 21, 20087 comments
Recently I was experimenting with complex down-conversion schemes. That is, generating an analytic (complex) version, centered at zero Hz, of a real bandpass signal that was originally centered at ±fs/4 (one fourth the sample rate). I managed to obtain one such scheme that is computationally efficient, and it might be of some mild interest to you guys. The simple complex down-conversion scheme is shown in Figure 1(a).

It works like this: say we have a real xR(n) input bandpass...

Dealing With Fixed Point Fractions

Mike January 5, 20163 comments

Fixed point fractional representation always gives me a headache because I screw it up the first time I try to implement an algorithm. The difference between integer operations and fractional operations is in the overflow.  If the representation fits in the fixed point result, you can not tell the difference between fixed point integer and fixed point fractions.  When integers overflow, they lose data off the most significant bits.  When fractions overflow, they lose data off...

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

Rick Lyons September 14, 201613 comments

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  ...

Amplitude modulation and the sampling theorem

Allen Downey December 18, 20156 comments

I am working on the 11th and probably final chapter of Think DSP, which follows material my colleague Siddhartan Govindasamy developed for a class at Olin College.  He introduces amplitude modulation as a clever way to sneak up on the Nyquist–Shannon sampling theorem.

Most of the code for the chapter is done: you can check it out in this IPython notebook.  I haven't written the text yet, but I'll outline it here, and paste in the key figures.


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.  

Curse you, iPython Notebook!

Christopher Felton May 1, 20124 comments


First, I think ipython is great. I use it daily and always have an ipython terminal open.  But just recently, I was showing off the ipython 0.12 notebook and in the process created a lengthy example while demonstrating the cool features of the ipython notebook.  The example included LaTeX equations, plots, etc.  Since the notebook session was on something of relevance I decided to clean up the session and use it for the beginning of a report.