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Mathematics of the Discrete Fourier Transform (DFT): with Audio Applications ---- Second Edition Paperback – April 13, 2007


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Mathematics of the Discrete Fourier Transform (DFT): with Audio Applications ---- Second Edition + Introduction to Digital Filters: with Audio Applications + Spectral Audio Signal Processing
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Product Details

  • Paperback: 322 pages
  • Publisher: W3K Publishing; 2 edition (April 13, 2007)
  • Language: English
  • ISBN-10: 097456074X
  • ISBN-13: 978-0974560748
  • Product Dimensions: 8.9 x 5.9 x 0.9 inches
  • Shipping Weight: 1.1 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #630,078 in Books (See Top 100 in Books)

Editorial Reviews

About the Author

Julius O. Smith is a research engineer and musician devoted to developing new technologies for music. He received the B.S.E.E. degree from Rice University, Houston, TX, in 1975 (Control, Circuits, and Communication). He received the M.S. and Ph.D. degrees in E.E. from Stanford University, Stanford, CA, in 1978 and 1983, respectively. His Ph.D. research was devoted to improved methods for digital filter design and system identification applied to music and audio systems. From 1975 to 1977 he worked in the Signal Processing Department at ESL, Sunnyvale, CA, on systems for digital communications. From 1982 to 1986 he was with the Adaptive Systems Department at Systems Control Technology, Palo Alto, CA, where he worked in the areas of adaptive filtering and spectral estimation. From 1986 to 1991 he was employed at NeXT Computer, Inc., responsible for sound, music, and signal processing software for the NeXT computer workstation. After NeXT, he became an Associate Professor at the Center for Computer Research in Music and Acoustics (CCRMA) at Stanford, teaching courses and pursuing research related to signal processing techniques applied to music and audio systems. Continuing this work, he is presently a Professor of Music and Associate Professor of Electrical Engineering (by courtesy) at Stanford University. For more information, see http://ccrma.stanford.edu/~jos/.

More About the Author

Julius O. Smith III teaches a music signal-processing course sequence and supervises related research at the Center for Computer Research in Music and Acoustics (CCRMA). He is formally a professor of music and associate professor (by courtesy) of electrical engineering at Stanford University. In 1975, he received his BS/EE degree from Rice University, where he got a good start in the field of digital signal processing and modeling for control. In 1983, he received the PhD/EE degree from Stanford University, specializing in techniques for digital filter design and system identification, with application to violin modeling. His work history includes the Signal Processing Department at Electromagnetic Systems Laboratories, Inc., working on systems for digital communications, the Adaptive Systems Department at Systems Control Technology, Inc., working on research problems in adaptive filtering and spectral estimation, and NeXT Computer, Inc., where he was responsible for sound, music, and signal processing software for the NeXT computer workstation. Prof. Smith is a Fellow of the Audio Engineering Society and the Acoustical Society of America. He is the author of four online books and numerous research publications in his field. For further information, see http://ccrma.stanford.edu/~jos/.

Customer Reviews

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I would certainly recommend this author to anyone wanting to learn this subject.
Ralston
I have read this book online and I am very impressed with the way the author explains the concepts.
V. Parasaram
Mr. Smith's books have been purely in the online realm unless you are an actual student of his.
calvinnme

Most Helpful Customer Reviews

13 of 13 people found the following review helpful By calvinnme HALL OF FAMETOP 500 REVIEWERVINE VOICE on January 30, 2008
Format: Paperback
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.
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4 of 4 people found the following review helpful By V. Parasaram on May 4, 2007
Format: Paperback
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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2 of 2 people found the following review helpful By sunil kumar behera on November 16, 2011
Format: Paperback Verified Purchase
This is a great book for beginners. It has everything explained to the tiny bit of details. I find it really helpful and will recommend it as a must read to everyone who is interested in Fourier transform.
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Professor Smith starts with the most fundamental concepts and introduces student to the concept of the " Nth Root of Unity". His use of the basic inner product ot two vectors to lead the reader into an intuitive understanding of the Discrete Fourier Transform is an elegant approach to teaching this subject. I would certainly recommend this author to anyone wanting to learn this subject. Professor Smith is an educator and that ability comes across in his book.
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By simonzz on February 9, 2014
Format: Paperback Verified Purchase
Professor O. Smith did a great job with this book.

If you want to learn the basis of DFT this book is for you.
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