The Fast Fourier Transform
In order to adapt the DFT for use with digital computers, the so-called Fast Fourier Transform (FFT) was developed. The FFT is simply an algorithm for calculating the DFT in a fast and efficient manner.
Cooley and Tukey are credited with the discovery of the FFT in 1967, but it existed much earlier, although without the digital computers needed to exploit it. The FFT algorithm places certain limitations on the signal and the resulting spectrum. For instance, the sampled signal to be transformed must consist of a number of samples equal to a power of two. Most FFT analyzers allow 512, 1024, 2048, or 4096 samples to be transformed. The frequency range covered by FFT analysis depends on the number of samples collected and on the sampling rate, as will be explained shortly.
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