Mathematics of the Discrete Fourier Transform (DFT): With Audio Applications

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Julius Smith, 2007 - Computers - 306 pages
2 Reviews
"The DFT can be understood as a numerical approximation to the Fourier transform. However, the DFT has its own exact Fourier theory, and that is the focus of this book. The DFT is normally encountered as the Fast Fourier Transform (FFT)--a high-speed algorithm for computing the DFT. The FFT is 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 others. In this book, certain topics in digital audio signal processing are introduced as example applications of the DFT"--Back cover.
 

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first 5 chapters are great

Contents

Introduction to the DFT
1
Complex Numbers
7
Proof of Eulers Identity
19
Sinusoids and Exponentials
31
Geometric Signal Theory
69
The DFT Derived
99
Fourier Theorems for the DFT
115
DFT Applications
165
Continuous Fourier Theorems
213
Sampling Theory
219
E Taylor Series Expansions
231
F Logarithms and Decibels
239
G Digital Audio Number Systems
251
H Matrices
265
MatlabOctave Examples
271
Bibliography
291

A Fast Fourier Transforms FFT
197
B ContinuousDiscrete Transforms
207

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