DFT Theorems Problems

See http://ccrma.stanford.edu/~jos/mdftp/DFT_Theorems_Problems.html

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 $ N$.8.2 The fastest FFT algorithms generally occur when $ N$ 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 $ N$ 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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