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The Scientist and Engineer's
Guide to Digital Signal Processing
by Steven W. Smith
California Technical Publishing
ISBN 0-9660176-3-3 (1997)
Chapter 8. The Discrete Fourier Transform
- The Family of Fourier Transforms
- Notation and Format of the DFT
- The Frequency Domain's Independent Variable
- DFT Basis Functions
- Synthesis, Calculating the Inverse DFT
- Analysis, Calculating the DFT
- Duality
- Polar Notation
- Polar Nuisances
Fourier analysis is a family of mathematical techniques, all based on decomposing signals
into sinusoids. The discrete Fourier transform (DFT) is the family member used with
digitized signals. This is the first of four chapters on the real DFT, a version
of the discrete Fourier transform that uses real numbers to represent the input and
output signals. The complex DFT, a more advanced technique that uses
complex numbers, will be discussed in Chapter 29. In this chapter we look at the
mathematics and algorithms of the Fourier decomposition, the heart of the DFT.
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