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The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in a (primal) domain (time, space) and the dual frequency domain. DFT requires an input sequence which is discrete, such as a sampling from an analogue audio signal.

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Direct calculation of the fft of a rectangular window

For a rectangular window defined as, the frequency spectrum equation and magnitude (or pseudo-magnitude) plot are, However, when I apply Scilab's fft() function or the definition of DFT definition to …
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