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…

Complex technology made real • Complex communications technology made easy
Complex To Real

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…

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…

Posted in Digital Communications

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,…

Posted in DFT

I have posted part 3 of the FFT tutorial at complextoreal.com.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…

Posted in Digital Communications

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,…

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…

I am going through my old material and am updating it. I have just uploaded FFT Part 1 after changing it in many places. http://complextoreal.com/chapters/fft1.pdf If you have comments on this tutorial (any including typos!), please post them here. Charan…

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 complextoreal.com and where I…

I have posted the final (nearly so) version of my MIMO tutorial. www.complextoreal.com It took a while. In the writing of this paper, I relied heavily on a few books and papers. The three books I often found myself thumbing…

Posted in MIMO tutorial

I have post a completed version of the MIMO tutorial on complextoreal.com.