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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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How can I take a fixed number of bins after N-point DFT when N is unknown?

My approach has been to take the input signal $x=(x_1,x_2,\ldots,x_N)$ and then find the one-sided amplitude spectrum from its N-point DFT: $\mathcal{F}(x) = (X_1, X_2, \ldots, X_N)$ $A(X)=(|X_1|, |X … This procedure gives me a 192-point DFT and a one-sided amplitude spectrum with 97 coefficients, which I interpolate to 51 (linear interpolation). …
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