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1 of 1 found the following review helpful:
Outstanding resource Feb 01, 2008
I have designed digital signal processing algorithms for twenty years. Having studied classic texts such as the Oppenheim and Schafer "Digital Signal Processing," I had a fairly good "technician's" understanding of how to use FFTs and design digital filters, or so I thought.
However, the underlying visual concepts eluded me. How do the signal analyzer outputs and Matlab plots really map to the complicated mathematics forming their foundation? Far too much was "left up to the reader," so forget the proofs and move on.
Then I encountered the Stanford University CCRMA resource created by Dr. Smith. I began to study the bite-sized chunks of core-course education on the DFT...a few chapters later, I was ready to add the hardcopies to my library.
As "Fretboard Logics" unlock the mysteries of guitar playing, so does this resource unlock the mathematics in terms that can be easily understood. Dr. Smith's instruction is revolutionary, a reformation in dissimenating knowledge all too carefully guarded by an academic elite. Is it a shame that a music department has to educate engineers in basic mathematical principles? No complaining...just buy the books!
2 of 2 found the following review helpful:
Very accessible book on the DFT Jan 30, 2008
I've got to hand it to two particular authors for bringing the subject of digital filters and its associated mathematics to musicians and the subject of music to engineers and computer scientists - Perry Cook and the author of this book, Julius O. Smith. Until recently only Mr. Cook's books have been in print. Mr. Smith's books have been purely in the online realm unless you are an actual student of his. Now two of his online publications are available for those of us interested in the practical details and mathematics of musical signal processing. There is this book, of course, and also the excellent "Introduction to Digital Filters with Audio Applications".
I've already read the two books in print - and skimmed through the dozens more Mr. Smith has on his website. The online access gives you a good idea of whether or not you want to purchase these books, but to get access to the problem sets you need the print version of the book. For the low price compared to other similar books, believe me it's worth it. The author works through both the proofs and motivations for the DFT, then goes on to show the reader some applications.
The Discrete Fourier Transform (DFT) is a numerical approximation to the Fourier transform. The DFT has its own exact Fourier theory, which is the main focus of this book. The DFT is normally encountered in practice as a Fast Fourier Transform (FFT), which is a high-speed algorithm for computing the DFT. FFTs are used extensively in a wide range of digital signal processing applications, including spectrum analysis, high-speed convolution (linear filtering), filter banks, signal detection and estimation, system identification, audio compression (such as MPEG-II AAC), spectral modeling sound synthesis, and many other applications. The only prerequisites for understanding this book is a good high school math background including some exposure to calculus. The following is an outline of the book's contents:
1. Intro to the DFT
2. Introduction to Complex Numbers - deals with factoring polynomials, the quadratic formula, the complex plane, and Euler's formula.
3. Proof of Euler's Identity - important when working with complex numbers.
4. Sinusoids and exponentials
5. Geometric Signal Theory - discusses the DFT a a change of coordinates from one basis set to another.
6. The DFT Derived
7. Fourier Theorems for the DFT
8. Example Applications of the DFT - shows practical FFT analysis in Matlab and Octave via examples.
There is also an appendix with some supplemental mathematical background material and some Matlab and Octave examples.
1 of 1 found the following review helpful:
An Excellent book for anyone interested in understanding DFT May 05, 2007
I have read this book online and I am very impressed with the way the author explains the concepts. The explanation is such that you will end up satisfied with both an intutive and mathematical understanding of DFT.
The book is very much self contained and not much is required as prerequisites. We are taken step by step from the basics to DFT.
Though I have read almost the entire book online I am eagerly waiting for my hardcopy order to arrive.
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