Fast Fourier Transform and Its Applications

By E. Brigham

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... This description may be from another edition of this product.

• Format: Paperback
• Language: English
• ISBN: 0133075052
• ISBN13: 9780133075052
• Release Date: April 1988
• Publisher: Pearson
• Length: 464 Pages
• Weight: 1.68 lbs.
• Dimensions: 1.0" x 6.0" x 8.9"

Customer Reviews

Outstanding classic

I am mainly a neurobiologist by training, but transform theory is very useful in visual neurobiology and visual psychophysics, and I've looked at and read dozens of books on various aspects of signal processing and transform theory. Much of this is surprisingly applicable to the brain science area, as the revolutionary work of David Marr and other scientists showed a quarter of a century ago. But getting back to the present book, this is one of the best books I've read in the signal analysis area. Brigham's presentation of various aspects of the FT, including the continuous FT, digital FT, convolution integrals, and so on, is clear and concise, whether he's discussing theory or applications. Also, his disussion of the Nyquist sampling theorem is the best and easiest to understand I've read. Interestingly, this theorem has quite practical applications, not just in digital sample theory, but in real life. According to the Nyquist theorem, no information is lost in converting from analog to digital form if the sampling frequency is twice that of the highest frequency in the signal. Well, have you ever used those audio headphones they have on commercial jetliners? The Nyquist theorem means they can switch the audio outputs at high frequency using well-known time-domain switching techniques rather than run copper to each passenger's seat. I've read that this saves 300 pounds of copper wire in a typical plane, the weight savings of which can of course be more profitably used for transporting other things. If you consider that 300 pounds is about the weight of your average couple, you can see how the savings would add up after even a few flights. But getting back to the book, I first encountered this work 20 years ago, and I'm delighted to see it's still around. My neurobiology student friends and I all got turned on to this book early in grad school, and it was a great help. I still fondly recall the many enjoyable hours we spent talking about how Fourier analysis and other techniques such as the Laplace transform, temporal modulation transfer fuction, two-dimensional convolution integrals, two-dimensional point-spread functons, filter techniques such as the finite and infinite response filters, Kalman filter, Hammond filter, and so on, could be applied to our area. And it all started with this book. It's a true classic that has never been exceeded for it's clear and concise exposition of a very important mathematical tool in both engineering and neurophysiology.

One of the best technical monographs.

I'm delighted to see that Brigham's book is in print. (I bought my first copy 20 years ago!) I'm planning to use as part of a course on signal processing. I've read several books on FT's and this is the best. It is one of the few technical books whose presentation is genuinely complete and clear. For example, the relationships between the discrete and the continuous FT, the role of the convolution integral, and the Nyquist theorem are presented logically with both algebraic proofs and graphical explanations. I'm always on the look out for monographs that focus on one subject and make you feel like you've become an expert on it when you're through. This fits the bill.

A Great Introduction to the FFT & How to Use It

Fourier transforms used to scare me. I got brain-lock, and couldn't even use them effectively in a package like Matlab or IDL. I got lost in integrals and delta functions and found myself rapidly sinking into mathematical quicksand. Evoking qliphotic demons from within a pentagram of power would have been simpler and less arcane.Then along came Brigham. Although his book had all the gnarly math of any other Fourier transform explanation I had ever seen, he also drew diagrams--diagrams which allowed me to "get" what the language of mathematics had so clearly expressed. All of a sudden the integrals were tamed. I wasn't in quicksand, just a damp sidewalk at Adventureland, waiting for the Jungle Cruise. And that was just the first couple of chapters! Brigham quickly moved into transform theory, applying the Fourier integral to convolution and correlation. Then into sampled waveforms and the discrete Fourier transform and its applications. Finally, he presented the Fast Fourier Transform. Once again, he clarifies without obfuscating. I found the FFT moving from the hyper-arcane to the land of "Well, duh!" (Beware: The actual FFT code included is not particularly efficient. Find source code for implementation *elsewhere*.) He extends the FFT to convolution and correlation, as well as to two dimensions. He doesn't skimp on applications, either. He clarifies interferometry, time-difference-of-arrival, power spectrum analysis, and beamforming. If you're not a signal processing wonk already, read this book. You may find it a powerful cure for DSP-phobia.

Excellent, A True Gem, Learn Signal Analysis & FFTs Here

This is an excellent, excellent text covering continuous and discrete-time signals/systems. Yes, it's ultimate focus is on the FFT, but about 50% of the content is basic continuous- and discrete-time signal analysis concepts, explained thoroughly, with superb graphic examples, and textual information from an obviously talented thinker, writer, communicator. It is extremely comprehensive but written 'patiently', bordering on the active voice style, which seems to be in short supply these days. If you had that well known and universally despised "S & S" textbook in college, torch it, buy this text, clean the slate, start over. There's no need to live with spectrophobia. This text has none of the usual inward, regurgitated extra-academic nonsense, the author clearly set out to write a fresh and original book. Read it slowly, the examples are vivid. You'll attain a visual feel for just what a linear transformation is, what the Fourier Transform is, and you'll develop the necessary intuition to allow you to be able to imagine both time and frequency domain relationships in a qualitative, systems oriented way (and this is where you want to be, trust me). The sections on convolution, correlation, discrete sampling, DFTs, finite-length effects, well, they're just perfect, with numerous mind-altering graphic examples. Many of these examples show side-by-side what happens in time and frequency domains simultaneously. It's clear that the author, unlike so many others, had a genuine interest in teaching and communicating. There's plenty of rigorous stuff if you want to go in deep, and I recommend it. The FFT sections are from the ground up - after a time you'll be able to design your own FT strategies and implement them with confidence. The best engineering text on the planet. Good Luck!

This is my favorite FFT reference.

I used the book to teach a Fourier Transform course for fellow engineers at Lockheed Martin. I taught straight from the book and only included some of my own personal FFT applications. The book gives a development of Fourier Transform & Series Fourier Transform, along with practical knowledge on how to apply them, and also gives numerous application at various level of difficulty. This is my favorite FFT reference. I'm still studying some of the applications in the last three chapters. I like the author's figures for showing the convolution integral using Fourier Transforms. All the concepts were shown graphical with figures. The publisher needs to print this book in hard back since I used my paper back edition so much that its coming apart.I also would recommend "Fourier-Related Transforms, Fast Algorithms and Applications" by Norman Morrison and "Introduction to Fourier Analysis" by Okan Ersoy as good academic references but lacked the application focus I was looking for.