Customer Reviews

The Fourier Transform and Its Applications

5 star:		(9)
4 star:		(2)
3 star:		(0)
2 star:		(2)
1 star:		(1)

 

 

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.

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 is an old classic in fourier analysis - it emphasizes intuitive understanding and uses images a lot to convey information, e.g. the book includes a pictorial dictionary of fourier transforms, and recommends using the method of dragging a strip of paper to get a better understanding of convolutions. The problems are challenging and very interesting, e.g. one problem asks the reader to explain the differences in spectra when reconstructing a signal by linear interpolation vs. sketching a smooth graph between the sample points by hand. (there are also easier problems for to begin with, before one tackles "engineering" questions as the one above) Highly recommended!

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.

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 <Give them a fish>. 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 <Teach them how to fish>.

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.

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.

Most of the positive reviews speak to the general good qualities of this book. I agree with them but, in addition, would like to point out that this book is way more than just a good intro to the subject for electrical engineers. As the author points out Fourier was not working on problems in electrical engineering, he was concerned with heat.

In the later part of the book, after introducing the mathematical properties of the FT and then their application in electrical engineering, the author considers heat and general conduction problems, as well as statistics, waveforms and noise. Bracewell shows clearly how the concepts,so useful for electical engineering are more general than traditonal EE aplications and can be used to acquire information, devise theories and solve problems in a variety of scientific endeavors.

Thus, the book is really comprehensive and will introduce the reader to the basics of FTs and their myriad applications in a variety of areas. This is a real strength of the author's and is a real positive for this book, either as a first text on FT, or as a reference to scientists and engineers working in any of the areas where the FT is routinely used.

When I came to the field of Fourier transform, the book provides me a clear, easy-understanding picture to the field so that I believe any of you can get into the field by use of the book. If you are looking for your first book to Fourier transform, don't waste your time, it is. Even through my life in the research, I depended on it most of the time. It's too great.

This book has a nice "intuitive" description of the Fourier integral pair and provides matching graphical representations/examples. With that being said, the book is loaded with typos when it comes to the equations, and the notation is not a standard mathematical or engineering notation; something in between. The author obviously understands the subject better than most, and provides reasoning for most of the notation, but there are so many errors ( in critical places ) that, in many cases, you must completely toss aside the provided explanation, and rework the examples from scratch ( probably not a bad idea with any book ). Long story short, if you're pretty familiar with the standard fourier integral coursework, you may find this book useful. If you're just learning the basics, go somewhere else or you'll regret it.

When I was a just neophyte graduate student, a famous electron microscopist recommended this book to me. Within its pages are so many elements that have proven to be incredibly useful. Certainly, one would expect that a detailed knowledge of Fourier transforms is essential to anyone doing research involving the imaging of a periodic object like the crystals studied by many of us in the electron microscopy community (as you would expect from Bloch's theorem). Bracewell provides easy to follow derivations of the theorems essential to the proper application of Fourier transforms and series to whatever problem may be at hand. It is also helpful that digital Fourier transforms are also explained--and in a way that is sufficiently explicit for performing actual calculations.

I should note that not only are Fourier transforms necessary for understanding dynamical diffraction theory (both Howie-Whelan and Cowley-Moodie), the study of electron energy loss spectroscopy (and the study of plasmon losses in particular) is significantly elucidated by a proper understanding of Fourier transforms. Much of the usefulness of Fourier transforms can be ascribed to the fact that the complicated convolution operation is reduced to simple multiplication by application of the Fourier transform!

The fact that Fourier transforms are useful in data reduction in general and image processing in particular is also considered in this book. The concept of aliasing is explored in sufficient detail--allowing the reader to determine to pixel density necessary in order extract the necessary information from a given image--an especially important consideration now that most transmission electron microscopy images are acquired digitally by CCD cameras.