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Mathematics of The Discrete Fourier Transform (DFT) with Audio Applications

12 years 1 months ago
Mathematics of The Discrete Fourier Transform (DFT) with Audio Applications
"The Discrete Fourier Transform (DFT) can be understood as a numerical approximation to the Fourier transform. However, 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) i.e., 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 (e.g., MPEG-II AAC), spectral modeling sound synthesis, and many other applications"
Julius O. Smith III
Added 04 Mar 2009
Updated 04 Mar 2009
Authors Julius O. Smith III

Table of Content

  1. Introduction to the DFT
  2. Introduction to Complex Numbers
  3. Proof of Euler's Identity
  4. Sinusoids and Exponentials
  5. Geometric Signal Theory
  6. The DFT Derived
  7. Fourier Theorems for the DFT
  8. Example Applications of the DFT 
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