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Understanding Digital Signal Processing, Third Edition by Richard G. Lyons

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Chapter Four. The Fast Fourier Transform

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Although the DFT is the most straightforward mathematical procedure for determining the frequency content of a time-domain sequence, it’s terribly inefficient. As the number of points in the DFT is increased to hundreds, or thousands, the amount of necessary number crunching becomes excessive. In 1965 a paper was published by Cooley and Tukey describing a very efficient algorithm to implement the DFT[1]. That algorithm is now known as the fast Fourier transform (FFT). Before the advent of the FFT, thousand-point DFTs took so long to perform that their use was restricted to the larger research and university ...

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