Why a DFT is usually called an FFT in practice
Practical implementations of the DFT are usually based on one of the Cooley-Tukey ``Fast Fourier Transform'' (FFT) algorithms [16].8.1 For this reason, the matlab DFT function is called `fft', and the actual algorithm used depends primarily on the transform length
.8.2 The fastest FFT algorithms
generally occur when is a power of 2. In practical audio signal
processing, we routinely zero-pad our FFT input buffers to the next
power of 2 in length (thereby interpolating our spectra somewhat) in
order to enjoy the power-of-2 speed advantage. Finer spectral
sampling is a typically welcome side benefit of increasing to the
next power of 2. Appendix A provides a short overview of some of the
better known FFT algorithms, and some pointers to literature and
online resources.
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FFT of a Simple Sinusoid
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Periodic Interpolation (Spectral Zero Padding)
