Abstract
The fast Fourier Transform (FFT) is an algorithm that increases the computation speed of the DFT of a sequence or its inverse (DFT) by simplifying its complexity. This is because by computing the DFT and IDFT directly from its definition is often too slow to be practical. Fourier analysis converts a signal from its original domain (time or space) into the frequency domain and vice versa. The DFT on the other hand is the decomposition of a sequence of values into components of different frequencies. For long data sets, in the thousands or millions, the reduction in computation time can be enormous. In the presence of round-off error, many FFT algorithms are much more accurate than evaluating the DFT definition directly. There are many FFT algorithms based on complex number arithmetic to number theory and group theory.
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