Chapter 13. Fast Fourier Transform

The discrete Fourier transform (DFT) plays an important role in many scientific and technical applications, including time series and waveform analysis, solutions to linear partial differential equations, convolution, digital signal processing, and image filtering. The DFT is a linear transformation that maps n regularly sampled points from a cycle of a periodic signal, like a sine wave, onto an equal number of points representing the frequency spectrum of the signal. In 1965, Cooley and Tukey devised an algorithm to compute the DFT of an n-point series in Θ(n log n) operations. Their new algorithm was a significant improvement over previously known methods for computing the DFT, which required Θ(n2) operations. ...

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