The Fourier Transform and Its Applications

I bought this book 7 years ago when i had to take graduate courses in FT theory in physics. After going through a number of FT books, i still find myself returning to it to refresh, learn, or for reference. The notation is definetly unique, but well worth the time to get used to it. For example, the sampling or replicating symbol "shah" (it looks like three spikes connected by a horizontal line at the bottom) represents an impulse train of equispaced delta functions. At first it seems that yet another symbol is barely needed (as if we didn't have enough already!), but i think that the ease with which sampling and basic theorems are demonstrated with this symbol justifies its invention. The book gravitates on discrete signals, but continuous signals are used throughout along with their discrete equivalents. The book is probably more theoretical than computational; a little bit more on the applied physics side than pure electrical engineering. I understand that this is an EE book, and i don't want to give you the impression that is a pure mathematical treatement of the subject. But i think it belongs to the era of seriously "grounded" EE books, and by "grounded" i mean on theoretical grounds. Even so, the reader will usually find very insightful discussions on "practical considerations." These considerations, however, are not of the "cookbook" approach. They are really embedded in a deeper theoretical framework. The figures are well chosen and superbly illustrative. Where theory gets heavy, a careful study of the pictures should clarify the concepts. Of particular interest is the last chapter (Ch. 22), a "Pictorial Dictionary of FTs" where you will find figures of some 70 functions and their FTs. Bracewell starts from the very basics and covers the fundamental theorems, the FT, DFT, DTFT, FFT algorithms, dynamic spectra, z-transform (briefly), Hartley and Laplace transforms, and then moves to applications like Antennas and Optics, Heat, Statistics, Noise, and Acoustics. The exercises are reasonable, but not easy. There are definetly alternatives to this book for beginners. But i think that Bracewell's perspective is unique and invaluable. Truely a timeless classic.

If you are looking for thorough explanations with great physical insight - this is the book to get. It is for people who want to know WHY more than HOW. However, If you are looking for how (to implement), I suggest the book "Fast Fourier Transform" by Brigham

This book by the Fourier monoply, Ronald Bracewell, is absolutely the best book on the Fourier transform. The concepts are very clearly illustrated with easily understood plain English. The whole complicated theory has been made so simple in this book. And more impressively, the whole book only employes very little complicated mathematics and still keep the theory complete and mathematically rigorous. When reading other books on Fourier theories, I always find the authors rely too much on the mathematical derivations to develope the theory and they themselves seem to not comprehend the essence of the theory. While in this book, Bracewell made every concept intuitively sensible. I will recommend every one who wants to learn Fourier theory to start from this book rather than any other books, which are usually rather confusing and not self-contained. You can get a 10 times deeper understanding on the whole theory with 10 times less difficulty.

I first was exposed to this book in 1965, in the form of galley proofs used by my new PhD teacher who had just finished Dr. Bracewell's first course. The Fourier, Hankel, etc. transforms are usually taught as 'black art', often by the unilluminated themselves . Dr. Bracewell lets in the light! An intuitive, necessary feel for the effects of the transforms and their inverses on the problem domain is presented, as well as a basis for the reader understanding this on his/her own . One hesitates to wax effusive over a text, but for 35 years the vision offered in this book has improved this writer's understanding of processes and situations ranging from refinery signal processing and queue theory to image enhancement on the Hubble Space Telescope (also a current work for Dr, Bracewell - the man never stops!). Buy it. Read it. Understand. Smile.

Provides a good coverage from an applied/engineering perspective rather than a pure/mathematical one. The introduction to non-standard analysis, and its application in linking the Fourier series and transform was a revelation. As was the ability to take the transform when all the preconditions are violated.