A Direct Digital Synthesizer with Arbitrary Modulus

Neil Robertson June 3, 20195 comments

Suppose you have a system with a 10 MHz sample clock, and you want to generate a sampled sinewave at any frequency below 5 MHz on 500 kHz spacing; i.e., 0.5, 1.0, 1.5, … MHz.  In other words, f = k*fs/20, where k is an integer and fs is sample frequency.  This article shows how to do this using a simple Direct Digital Synthesizer (DDS) with a look-up table that is at most 20 entries long.   We’ll also demonstrate a Quadrature-output DDS.  A note on...

Somewhat Off Topic: Deciphering Transistor Terminology

Rick Lyons May 28, 20193 comments

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

Rick Lyons May 24, 20195 comments

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

Rick Lyons May 20, 20199 comments

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....

IIR Bandpass Filters Using Cascaded Biquads

Neil Robertson April 20, 201911 comments

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...

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

Rick Lyons March 29, 201922 comments

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...

Generating Partially Correlated Random Variables

Harry Commin March 23, 201910 comments
IntroductionIt is often useful to be able to generate two or more signals with specific cross-correlations. Or, more generally, we would like to specify an $\left(N \times N\right)$ covariance matrix, $\mathbf{R}_{xx}$, and generate $N$ signals which will produce this covariance matrix.

There are many applications in which this technique is useful. I discovered a version of this method while analysing radar systems, but the same approach can be used in a very wide range of...

Free Goodies from Embedded World - Full Inventory and Upcoming Draw Live-Streaming Date

Stephane Boucher March 22, 20191 comment

Chances are that you already know that I went to Embedded World a few weeks ago and came back with a bag full of "goodies".  Initially, my vision was to do a single draw for one person to win it all, but I didn't expect to come back with so much stuff and so many development kits.   Based on your feedback, it seems like you guys agree that It wouldn't make sense for one person to win everything as no-one could make good use of all the boards and there would be lots of...

Angle Addition Formulas from Euler's Formula

Cedron Dawg March 16, 20198 comments

This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT), but only indirectly. The main intent is to get someone who is uncomfortable with complex numbers a little more used to them and relate them back to already known Trigonometric relationships done in Real values. It is essentially a followup to my first blog article "The Exponential Nature of the Complex Unit Circle".

Polar Coordinates

The more common way of...

Demonstrating the Periodic Spectrum of a Sampled Signal Using the DFT

Neil Robertson March 9, 201920 comments

One of the basic DSP principles states that a sampled time signal has a periodic spectrum with period equal to the sample rate.  The derivation of can be found in textbooks [1,2].  You can also demonstrate this principle numerically using the Discrete Fourier Transform (DFT).

The DFT of the sampled signal x(n) is defined as:

$$X(k)=\sum_{n=0}^{N-1}x(n)e^{-j2\pi kn/N} \qquad (1)$$


X(k) = discrete frequency spectrum of time sequence x(n)

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: http://www.signumconcepts.com/IP_center/paper018.pdf

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...

Design IIR Bandpass Filters

Neil Robertson January 6, 201810 comments

In this post, I present a method to design Butterworth IIR bandpass filters.  My previous post [1] covered lowpass IIR filter design, and provided a Matlab function to design them.  Here, we’ll do the same thing for IIR bandpass filters, with a Matlab function bp_synth.m.  Here is an example function call for a bandpass filter based on a 3rd order lowpass prototype:

N= 3; % order of prototype LPF fcenter= 22.5; % Hz center frequency, Hz bw= 5; ...

Linear-phase DC Removal Filter

Rick Lyons March 30, 200825 comments

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...

Design IIR Filters Using Cascaded Biquads

Neil Robertson February 11, 201824 comments

This article shows how to implement a Butterworth IIR lowpass filter as a cascade of second-order IIR filters, or biquads.  We’ll derive how to calculate the coefficients of the biquads and do some examples using a Matlab function biquad_synth provided in the Appendix.  Although we’ll be designing Butterworth filters, the approach applies to any all-pole lowpass filter (Chebyshev, Bessel, etc).  As we’ll see, the cascaded-biquad design is less sensitive to coefficient...

Frequency-Domain Periodicity and the Discrete Fourier Transform

Eric Jacobsen August 6, 2012


Some of the better understood aspects of time-sampled systems are the limitations and requirements imposed by the Nyquist sampling theorem [1]. Somewhat less understood is the periodic nature of the spectra of sampled signals. This article provides some insights into sampling that not only explain the periodic nature of the sampled spectrum, but aliasing, bandlimited sampling, and the so-called "super-Nyquist" or IF sampling. The approaches taken here include both mathematical...

A Differentiator With a Difference

Rick Lyons November 3, 20078 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...

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...

Digital PLL's -- Part 1

Neil Robertson June 7, 201622 comments
1. Introduction

Figure 1.1 is a block diagram of a digital PLL (DPLL).  The purpose of the DPLL is to lock the phase of a numerically controlled oscillator (NCO) to a reference signal.  The loop includes a phase detector to compute phase error and a loop filter to set loop dynamic performance.  The output of the loop filter controls the frequency and phase of the NCO, driving the phase error to zero.

One application of the DPLL is to recover the timing in a digital...

Generating pink noise

Allen Downey January 20, 20161 comment

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...

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 DSPRelated.com 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.

edit - video of the event:

I currently have two jobs: one as an electrical/dsp engineer recycled as a web publisher and the other...

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:http://www.dsprelated.com/documents.phpThere 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 ( 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

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...