An accessible examination of the FFT great for self study

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	• Fast Fourier Transform and Its Applications (Prentice-Hall Signal Processing Series) E. Brigham Prentice Hall, 1988 - 416 pages average customer review:based on 14 reviews view larger image
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highly recommended

Very good, but be careful, though

The book I have is ISBN 0-13-307496. It was published in 1974.

I am very happy about this book, I first read it in 1979 when I was 19, and I found it really marvellous. I agree with the other reviewers, but I must add a note of caution - the edition I have contains some errors. They are as follows;

p155, p157 - the factors w(11) and w(10) are incorrectly placed on the butterfly diagram 10.3 and 10.4 respectively,

p166, p168, p169, equations 10-26 and most equations following to the end of the chapter - the factors R(N-n) and I(N-n) should be R(N-1-n) and I(N-1-n), respectively.

I hope I'm right about this, but the convention is that the indices are from 0 to N-1, and therefore if n=0, then N-n is N - which not an allowed index.

Apart from these sort of errors (I havn't been through the whole book with a fine toothcomb), its really very good, actually extraordinarily clear.

One of its main benefits is that it doesn't veer away from the FFT to the very complicated developments such as fractional transforms and other developments which might confuse the sort of audience it's aimed at (which is definitely the graduates).

But if you want to look deeply into FFTs for a real application you will need a lot more. I must mention,for instance, that the implementation of an FFT needs fairly careful error propagation and rounding analysis, and this isn't covered at all in the book. Neither are prime factor FFTs. In fact the chapter "FFT algorithms for arbirary factors" is only a method of factoring into powers of two, and certainly not the prime factor decomposition which was developed later by Winograd, Chuo, and others.

It must also be said that while the DCT is practically a kissing cousin of the FFT, this naturally isn't covered in this text... but neither are the finite field implementations that are now taking many peoples imaginations to faster and faster FFTS.

Also, there are jolly useful things to know about, such as the FFT when you only need a subset of the output data points. There are pruning algorithms which greatly simplify the computations.

But it's very good as a starter, I wouldn't do without my copy!

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Written with the reader in mind.

I think this is one of the most understandable books in signal processing that I've ever come across. I get the feeling that Brigham had been frustrated by technical texts that were poorly written, and decided he wasn't going to commit the same sin. Plenty of carefully planned illustrations designed to help the reader start from a known place, and move step-by-step to an understanding of something new. Not just a bunch of faceless equations. I think this would be an excellent college text.

Like any in-depth text dealing with a mathematically complex topic, there appear to be a number of mistakes left in to keep the reader on his/her toes. But fewer than most. I highly recommend this book, even though I'm usually a pretty tough critic. I too have been frustrated by too many poorly written books.

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The best

This book provides excellent intuition into the fourier transform, discrete fourier transform, and fast fourier transform. There are no others that provide the depth of intuition.

If a reader should find it difficult, then he/she should be satisfied that the struggle is worth it and will lead to an exceptional understanding of the subject matter. All complaints are unjustified (though it might be nice if Brigham treated the Z transform as well).

The Best DFT / FFT Book on the Market

I purchased the first edition of this book way back on January 10, 1975, when I was young design engineer, just breaking into the Digital Signal Processing business. I bought the book at the Stanford University Book store for a whopping $19.95. The receipt is still in the book.

The book was considered to be a DSP industry bible back then, and in my opinion, it is still the best DFT/FFT book on the market today.

Mr. Brigham seems to be very detailed oriented. He methodically progresses from one subject to the next and explains each topic in a clear and concise manner. The book is loaded with extremely detailed graphics that give the reader a very good picture of the operation, properties, and mechanics of the Discrete Fourier Transform. His mathematical derivations of various DFT/FFT properties are straight forward and can be read and understood in short order.

I consider Mr. Brigham's book to be an essential engineering resource. I have relied upon, and utilized the information provided in this book for over 30 years of successful DSP design.

If I ever misplace my time worn book, would I purchase it again? The answer is a definite yes. The money is well spent.

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An accessible examination of the FFT great for self study

This book is not just another terse math or signal processing book. It tries to provide an alternative to standard DSP techniques that develop the FFT adequately enough, but show nothing about applications and have the student believing that "The Butterfly Element" is something he can buy an armful of at an electronics store and assemble. All developments in this book use graphical techniques and examples that insure clarity in the presentation. The book provides not only a readable introduction to the FFT but a thorough and unified reference for applying it to various fields of interest. It is great for self-study. The text is divided into five major subject areas:

1. The Fourier Transform and its properties
2. The Discrete Fourier Transform - It is developed from the continuous Fourier Transform both graphically and theoretically. Its properties are examined as are numerous waveform classes via illustrative examples. Discrete convolution and correlation are defined and compared with the continuous equivalents via examples.
3. The FFT - The FFT algorithm is developed along with an explanation of why the FFT is efficient. Computer programs are developed that can calculate the FFT.
4. Basic Applications of the FFT - Presents the application of the FFT to the computation of discrete and inverse discrete Fourier transforms. There is an emphasis on graphical examination of resolution and common FFT user mistakes such as aliasing, time domain truncation, noncausal time functions, and periodic functions. The applications examined include Laplace transform computation, discrete convolution and correlation, and two-dimensional Fourier transform convolution. Computer programs are provided.
5. Signal Processing and System FFT Applications - The design and application of digital filters using the FFT are explored. A novel application of the FFT to multichannel band-pass filtering is developed in a way that can readily be expanded by the reader.

I highly recommend this book to readers who want a complete explanation and investigation of the FFT and its applications that is clear enough for self-study.

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reviews: page 1, 2, 3

The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.

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