9 of 9 people found the following review helpful:
4.0 out of 5 stars
Varied, specific, and practical., December 4, 2004
This review is from: Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms (Computational Mathematics) (Hardcover)
If you need this book, you already know it. You barely remember what the Fourier transform does, let alone how it works, and you need to implement it from scratch. This book is for you.
Most programmers never need to use Fourier transforms. Most of the ones who do will get by quite nicely on black boxes from Mathematica, Matlab, or Numerical Recipes. Data goes in, answers come out, and "a miracle occurs" somewhere in between. There are those times, however, when you can't use the canned routines. You just have to write your own.
This book isn't for the faint-hearted, but really does give everything a non-specialist needs for creating a competent implementation. There's no cut&paste code here, but this is for people with unique needs. It presents a number of basic variations, with clear illustrations and pseudocode. It even discusses 2D transforms, but most of that discussion centers on how to transpose the 2D matrix between 1D transforms.
The discussion of parallel implementation was the only section I found weak. It's aimed at standard sorts of multiprocessors, with specific kinds of connection networks between processors. First, those networks are rare in commercial multiprocessors or are so deeply embedded that the topology is not accessible to the application writer. Second, those networks and architectures miss a lot of important computing environments completely - including the ones important to me.
I don't wish it on anyone, but it might happen - you might have to implement a FFT for yourself. If it does happen, this book may be your most effective tool. It will probably take the non-specialist (like me) time to get past some of the notation, but the answers here are worth the effort.
//wiredweird
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2 of 2 people found the following review helpful:
4.0 out of 5 stars
What the title suggests, November 4, 2007
This review is from: Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms (Computational Mathematics) (Hardcover)
Personally, I am satisfied with what I bought. I wrote an uninspired fast fourier transform from its mathematical formula and it took 30 seconds to execute. I knew I could do better. After buying the book I learn to play close attention to the bit reversal on the twiddles (trig functions). I also learned how to do the split-radix. I also learned that each calculation yields two terms. Also, I gained emough of a sense of how the fft works that I was able to successfully create threads and try parallel processing. All totalled, I reduced the run time from 30 seconds to 1 second.
The book was not as well written as I would have liked. The formula for the split-radix was screwed up. Using the form of the formula and the suggestion of what it represented I was able to derive the formula. It would have been nice if they had written out each term of each iteration for a 64-term fft. That is what I did to see with my own eyes what was happening. The text is too abstract.
All-in-all it was worth the $100.
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1 of 10 people found the following review helpful:
3.0 out of 5 stars
More "Dirty" Math, compliments of Chu et alii., March 10, 2006
This review is from: Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms (Computational Mathematics) (Hardcover)
While I'm positive that this book will serve engineers well, I cannot recommend it to practitioners of pure mathematics, videlicit those who are not comfortable with the bloodied abortion that is mathematics to the engineer. It blows my mind that we ever got a man on the moon! A good example can be found in the first line of page 7. omega^l=omega^(l+(2*n+1)). Keep in mind that n is an element of the set of positive integers, their claim not mine. Now, if you solve for n you'll find that this equation can only be satisfied for n=-1/2, clearly not an element of Z+! (Perhaps rational numbers are included in the set of "integers for engineers.") And yet they seem to indicate that it holds for all n in the aforementioned set! I pray that I've missed something and that someone will embarrass me by pointing out my mistake because as irate as I am right now, blood will likely shoot out of my nose in the next 5 minutes and they'll find me dead in my office at day's end.
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