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Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation by C. Britton Rorabaugh

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Note 13. Discrete Fourier Transform

The discrete Fourier transform (DFT) is perhaps the single most important mathematical tool in all of DSP. Unlike many other Fourier analysis techniques that can be applied only to signals that are expressed in the form of mathematical functions, the DFT can be implemented in practical systems to analyze sampled real-world signals numerically. The DFT also plays a role in certain types of filter design as well as in the efficient implementation of filter banks, transmultiplexers, and demodulators for multi-frequency communication signals such as orthogonal frequency division multiplexing (OFDM).

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