Abstract
The discrete Fourier transform (DFT) is a method that represents the frequency content of a finite length time sequence, or sequence of samples. The discovery of fast methods for computing the DFT, called fast Fourier transforms, has led to the widespread use of the DFT and has established digital signal processing as a major research and application area. The DFT is very closely related to the discrete Fourier series (DFS). The DFS represents a periodic discrete time sequence as a linear combination of complex exponentials. In contrast to the DFS, the DFT can be interpreted as a linear transformation from one finite length sequence to another. The DFT can be viewed as a frequency-sampled version of the discrete time Fourier transform (DTFT). The chapter discusses how the DFT relates to other Fourier transforms, and its interpretation from a sampled DTFT as well as a linear algebraic standpoint.
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