Feedback Controllers - Making Hardware with Firmware. Part 7. Turbo-charged DSP Oscillators

Steve Maslen January 5, 20187 comments
This article will look at some DSP Sine-wave oscillators and will show how an FPGA with limited floating-point performance due to latency, can be persuaded to produce much higher sample-rate sine-waves of high quality. 

Comparisons will be made between implementations on Intel Cyclone V and Cyclone 10 GX FPGAs. An...

Linear Feedback Shift Registers for the Uninitiated, Part XII: Spread-Spectrum Fundamentals

Jason Sachs December 29, 20171 comment

Last time we looked at the use of LFSRs for pseudorandom number generation, or PRNG, and saw two things:

  • the use of LFSR state for PRNG has undesirable serial correlation and frequency-domain properties
  • the use of single bits of LFSR output has good frequency-domain properties, and its autocorrelation values are so close to zero that they are actually better than a statistically random bit stream

The unusually-good correlation properties...

An Efficient Linear Interpolation Scheme

Rick Lyons December 27, 201723 comments

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. ...

An Alternative Form of the Pure Real Tone DFT Bin Value Formula

Cedron Dawg December 17, 2017

This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by deriving alternative exact formulas for the bin values of a real tone in a DFT. The derivation of the source equations can be found in my earlier blog article titled "DFT Bin Value Formulas for Pure Real Tones"[1]. The new form is slighty more complicated and calculation intensive, but it is more computationally accurate in the vicinity of near integer frequencies. This...

Design IIR Butterworth Filters Using 12 Lines of Code

Neil Robertson December 10, 20176 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:

Feedback Controllers - Making Hardware with Firmware. Part 6. Self-Calibration Related.

Steve Maslen December 3, 20177 comments

This article will consider the engineering of a self-calibration & self-test capability to enable the project hardware to be configured and its basic performance evaluated and verified, ready for the development of the low-latency controller DSP firmware and closed-loop applications. Performance specifications will be documented in due course, on the project website here.

  • Part 6: Self-Calibration, Measurements and Signalling (this part)
  • Part 5:

Simplest Calculation of Half-band Filter Coefficients

Neil Robertson November 20, 2017

Half-band filters are lowpass FIR filters with cut-off frequency of one-quarter of sampling frequency fs and odd symmetry about fs/4  [1]*.  And it so happens that almost half of the coefficients are zero.  The passband and stopband bandwiths are equal, making these filters useful for decimation-by-2 and interpolation-by-2.  Since the zero coefficients make them computationally efficient, these filters are ubiquitous in DSP systems.

Here we will compute half-band...

Feedback Controllers - Making Hardware with Firmware. Part 5. Some FPGA Aspects.

Steve Maslen November 14, 2017
This part of the on-going series of articles looks at a variety of aspects concerning the FPGA device which provides the high-speed maths capability for the low-latency controller and the arbitrary circuit generator application. In due course a complete specification along with  application  examples will be maintained on the project website here.

Improved Three Bin Exact Frequency Formula for a Pure Real Tone in a DFT

Cedron Dawg November 6, 2017

This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by extending the exact two bin formulas for the frequency of a real tone in a DFT to the three bin case. This article is a direct extension of my prior article "Two Bin Exact Frequency Formulas for a Pure Real Tone in a DFT"[1]. The formulas derived in the previous article are also presented in this article in the computational order, rather than the indirect order they were...

There's No End to It -- Matlab Code Plots Frequency Response above the Unit Circle

Neil Robertson October 23, 20179 comments
Reference [1] has some 3D plots of frequency response magnitude above the unit circle in the Z-plane.  I liked them enough that I wrote a Matlab function to plot the response of any digital filter this way.  I’m not sure how useful these plots are, but they’re fun to look at. The Matlab code is listed in the Appendix. 

This post is available in PDF format for easy...

Polyphase Filters and Filterbanks

Kyle March 20, 20138 comments


Polyphase filtering is a computationally efficient structure for applying resampling and filtering to a signal. Most digital filters can be applied in a polyphase format, and it is also possible to create efficient resampling filterbanks using the same theories.

This post will walk through a reference implementation of both the downsampling polyphase filter and a downsampling polyphase filterbank using scipy, numpy, matplotlib, and python. It should also highlight some of...

Pulse Shaping in Single-Carrier Communication Systems

Eric Jacobsen April 10, 200833 comments

Some common conceptual hurdles for beginning communications engineers have to do with "Pulse Shaping" or the closely-related, even synonymous, topics of "matched filtering", "Nyquist filtering", "Nyquist pulse", "pulse filtering", "spectral shaping", etc. Some of the confusion comes from the use of terms like "matched filter" which has a broader meaning in the more general field of signal processing or detection theory. Likewise "Raised Cosine" has a different meaning or application in this...

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

Eric Jacobsen May 29, 20122 comments


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...

Polyphase filter / Farrows interpolation

Markus Nentwig September 18, 200713 comments


this article is meant to give a quick overview over polyphase filtering and Farrows interpolation.

A good reference with more depth is for example Fred Harris' paper:

The task is as follows: Interpolate a band-limited discrete-time signal at a variable offset between samples.In other words:Delay the signal by a given amount with sub-sample accuracy.Both mean the same.

The picture below shows samples (black) representing...

Frequency Dependence in Free Space Propagation

Eric Jacobsen May 14, 20088 comments


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...

Time Machine, Anyone?

Andor Bariska March 7, 20086 comments

Abstract: Dispersive linear systems with negative group delay have caused much confusion in the past. Some claim that they violate causality, others that they are the cause of superluminal tunneling. Can we really receive messages before they are sent? This article aims at pouring oil in the fire and causing yet more confusion :-).

PDF version of this article.


In this article we reproduce the results of a physical experiment...

Understanding and Implementing the Sliding DFT

Eric Jacobsen April 23, 20154 comments

In many applications the detection or processing of signals in the frequency domain offers an advantage over performing the same task in the time-domain.   Sometimes the advantage is just a simpler or more conceptually straightforward algorithm, and often the largest barrier to working in the frequency domain is the complexity or latency involved in the Fast Fourier Transform computation.   If the frequency-domain data must be updated frequently in a...

A Differentiator With a Difference

Rick Lyons November 3, 20076 comments

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...

Linear-phase DC Removal Filter

Rick Lyons March 30, 200823 comments

This blog describes several DC removal networks that might be of interest to the 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...

Accurate Measurement of a Sinusoid's Peak Amplitude Based on FFT Data

Rick Lyons December 14, 201110 comments

There are two code snippets associated with this blog post:

Flat-Top Windowing Function for the Accurate Measurement of a Sinusoid's Peak Amplitude Based on FFT Data


Testing the Flat-Top Windowing Function

This blog discusses an accurate method of estimating time-domain sinewave peak amplitudes based on fast Fourier transform (FFT) data. Such an operation sounds simple, but the scalloping loss characteristic of FFTs complicates the process. We eliminate that complication by...

DSPRelated and EmbeddedRelated now on Facebook & I will be at EE Live!

Stephane Boucher February 27, 20148 comments

I have two news to share with you today.

The first one is that I finally created Facebook pages for and EmbeddedRelated (DSPRelated page - EmbeddedRelated page). For a long time I didn't feel that this was something that was needed, but it seems that these days more and more people are using their Facebook account to stay updated with their favorite websites. In any event, if you have a Facebook account, I would greatly appreciate if you could use the next 5 seconds to "like"...

Collaborative Writing Experiment: Your Favorite DSP Websites

Stephane Boucher May 30, 2013

You are invited to contribute to the content of this blog post through the magic of Google Docs' real time collaboration feature.

I discovered this tool several months ago when I was looking for a way to coordinate our annual family halloween party (potluck) and avoid the very unpleasant situation of ending up with too much chips and not enough chocolate (first world problem!).  It was amusing to keep an eye on the "food you will bring" document we had created for this and watch...

DSPRelated Finally on Twitter!

Stephane Boucher February 20, 20132 comments


It's been a while since you've heard from me - and there are many reasons why:

1 - I've made a clown of myself (video here)

2 - I've been working on unifying the user management system.  You can now participate to the three related sites (DSPRelated, FPGARelated and EmbeddedRelated) with only one account (same login info). 

3- I've been working on getting up to speed with social networks and especially Twitter.   I have resisted the idea for a while - at 40...

Two jobs

Stephane Boucher December 5, 201223 comments

For those of you following closely embeddedrelated and the other related sites, you might have noticed that I have been less active for the last couple of months, and I will use this blog post to explain why. The main reason is that I got myself involved into a project that ended up using a better part of my cpu than I originally thought it would.

I currently have two jobs: one as an electrical/dsp engineer recycled as a web publisher and the other as a parent of three kids. My job...

Do you like the new Comments System?

Stephane Boucher September 19, 20124 comments

I have just finished implementing a new comments system for the blogs.  Do you like it?

Please share your thoughts with me by adding a comment.

I'll wait a few days and make sure it works properly and then I'll port it to the code snippets and papers section.


DSP Papers, Articles, Theses, etc

Stephane Boucher March 17, 20111 comment

As you may already know, there is a 'Papers and Theses' section on DSPRelated: are hundreds of DSP Related documents (articles, papers, theses, dissertations, etc) scattered all around the web, and the goal with this section is to find and list as many of those documents as possible in one place. There are, at the moment, a little over 100 documents listed, which I believe is only a small subset of what is available out there, and I need your help...

Code Snippets Suggestions

Stephane Boucher January 19, 20115 comments

Despite being only a couple of months old, the Code Snippet section ( ) 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

Stephane Boucher December 1, 2010

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

Stephane Boucher November 2, 20101 comment

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!

Stephane Boucher October 15, 201012 comments

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.  


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...