I have added a new tutorial on Fourier transform. I have taken a different approach than what I had previously. I think it is still tilted towards making the concept simpler so it tends to dwell less on on typical textbook items such as convergence conditions and properties. Most of you reading my tutorials already have formal education in this area so I am concentrating only on making the ideas clear and hopefully more intuitive.
I recently came across a textbook, "Continuous and Discrete Time signals and Systems" by Mrinal Mandal and Amir Asif. Dr. Mandal is a professor at University of Alberta, Edmonton Canada and Dr. Asif is a professor at York University in Toronto. This is an excellent book. The balance is more on theory as it should be for a textbook but it does a superb job of making the theory crystal clear with unambiguous use of variables and terms, repeating these as needed and keeping obfuscation at bay. The authors go over examples in great detail with graphs (which are beautiful by the way. I am always struggling with graphs in my write-ups.), explaining the smallest steps in the working of examples and trying to make the material comprehensible from both the practical and didactic viewpoint. It covers a very large range of topics, Laplace transforms, Z transform, filter design and as such it is a large book. However all expositions are very well done and will add to intuitive understanding of this topic. If you are working in DSP and need to refer to the basics, then this would be a really good book to have on your shelf. Otherwise for any professors reading this, I suggest that you seriously consider this as a textbook for your Signals and Systems class.
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 includes Matlab code.
Let me know if I succeeded in making this topic easy(er) to grasp.
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.
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.
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.
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 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.
I use this blog to announce changes and publications related to my digital communications tutorials at www.complextoreal.com
I also write children's math and reading books (The Reading Lesson and Verbal Math Lesson series) which can be seen on Amazon.com. Please consider buying these books for your children.