Digital communications tutorial links

I recently changed to this WordPress format for Although the functionality is great, the old links which so many schools, colleges had no longer work.

The site has fallen off totally from Google, probably because none of the old links can be found by Google. Hopefully their robots will find this new address.

In the meanwhile, a direct link from your site to mine will help a lot.

If you know of any good engineering tutorial sites, please also let me know.


Charan Langton

DTFT, DFT Tutorial added

I have added Chapter 5 which covers DFT and DTFT and a little bit about FFT.  The tutorial has most of the Matlab code used to generate the graphs. In the links page, I have also added the sites I referred to. Most of them are very good.

Once you dive into the topic, you realize how simple on hand but then so complex at the same time, kind of like Life, I guess. The next topic on the list is Windows. Use of Windows is almost mandatory when doing DFT on real signals. So understanding how to use them is as important as the DFT itself.

Charan Langton

April 3, 2013



Understanding Digital Signal Processing by Richard Lyons

In every field there are books that just stand apart. They are so well written that they change your opinion about the subject. In fact, with most mathematical ideas if you understand them well, they no longer seem tedious, or hard. Richard Lyons book “Understanding Digital Signal Processing” is just such a book. I remember coming across it on Amazon when Amazon was young. This was before Amazon had a “look inside” feature and one was generally leery of ordering things on line. There was a two page introduction to the book which I read. The writing style was impressive and so I ordered the book. I still remember looking through and thinking this looks fun! It had more pictures than it had formulas!

I read the first chapter that night and felt exhilarated. I had my first aha moment in DSP. Although I was out of graduate school for several years at that time, I felt that I had never really understood the subject. Yes, I could do the transforms for homework etc., but understood, not really. In this book, Lyons starts with discrete signals, goes through sampling and aliasing in the first chapter. Each chapter build gently on the previous. All just a model of clarity and beauty. I particularly loved the filter chapter, with such easy to understand exposition of what the equation meant, the forward part and the reverse part. We all love pictures and the book’s strength is its ability to communicate not just in words but also in figures. From DFT to filter design to DSP algorithms, all come alive as explained by Lyons.

I think I did read the whole book in about a week. I then flipped to the end to see who this guy was. It turned out that he worked locally at TRW. So hesitatingly, I called him to tell him how much I loved his book. He became my role model and a friend. I had been writing papers and felt that this is the way engineering should be taught. This is the way engineering books should be written. With the student in mind. No hiding behind formulas.

I recently picked up the book again as I am writing some papers on FFTs. And despite being somewhat smarter today than 15 yeas ago, I find the book still a model of engineering writing. Just a plain excellent book, deserving of all the superlatives I can muster. Fantastic, etc. etc. If you are a student in this field or an engineer, I recommend that you add this book to your library immediately.

If you have read this book, would love to hear what you think of it.

-Charan Langton


Folding and Aliasing

Here is an java applet which lets you see the effect of sampling frequency and reconstruction of the signal. The signal is sampled, then goes through a low pass. You will see here what happens when sampling frequency is not large enough and the replicated spectrum overlap.

Requires Java.

New look

In coming to this new format, I had to leave behind the board which has over 2000 members. There were quite a lot of people on it and I am sorry that it will not be accessible any more. However, this format may work even better, as now the discussions will be grouped by topic. For general questions, help etc. from others, please use the main page.

I may add a forum, if there is interest
Thank you.

Discrete-time Fourier Series and Fourier Transform

I have posted part 3 of the FFT tutorial at
It starts with the development of discrete signals, their properties, periodicity of discrete signals,
finding a set of basis harmonics and then finally the Discrete-time Fourier Transform.

The tutorial also includes Matlab code.
Let me know if I succeeded in making this topic easy(er) to grasp.


Fourier Made easy part 2 – new version uploaded

I have uploaded a new version of the Fourier Made Easy part 2 tutorial. In this version, I have included more examples as well as Matlab code to plot some of the key pictures.  I get requests to include code, so I am going through my old work and including it as I can. I use Coware SPW for most of my “real” work and from it I can only include the pictures. Its purely block orientated and has no code to share.

This tutorial can be used for classroom use as well for anyone wanting to brush up on transform theory.
I am now helped in my work by Victor Levin, my son. He did the Matlab codes in this tutorial. Victor is a graduate student in EE at Georgia Tech. He is currently a TA at the Metz, France campus of GTech.

I recently went to France and saw the GTech campus and facilities. Very nice!

Charan Langton
October, 2012

Video that explains the complex exponential

While writing the second part of the Fourier tutorial, I came across this video which does a great job of explaining the complex exponential, its relationship to sinusoids and hence to the reason why signal processing math is done with exponentials. Nicely done.

Fourier tutorial part 1 – updated

I am going through my old material and am updating it. I have just uploaded FFT Part 1 after changing it in many places. If you have comments on this tutorial (any including typos!), please post them here. Charan Langton

Thanks to The Mathworks

The Mathworks company has just provided me a complementary copy of Matlab out of their “Author” program. So I want to take this space to thank them. For may of the demonstrations in my tutorials on and where I feel it necessary to pass on the code, I use Matlab. I have also started using Simulink and am beginning to make progress. I will make some of my Matlab models available with my communications tutorials. Progress on the book is slow. But in the meantime, please feel free to send me comments and errors you find. Thank you Naomi Fernandes and The Mathworks. Charan Langton

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