Abstract
This chapter elaborates the faster Fourier transform. The fast Fourier Transform algorithms have been explored pretty thoroughly, and vary from quite terse to highly optimize. There is one task common to every in-place algorithm that can be made faster, namely, the flipped bit count shuffling of data that occurs before, or after the transform proper. Historically, folks have tried to come up with clever ways either to flip the bits of an ordinary counter or to make a flipped counter and but there is another possibly pointed out by Evans. First, all rearrangements involve simply swapping pairs and second, that some indices do not change. Both these properties hold in larger cases as well, and suggest trying to generate only the pairs that must be swapped. It is found that for a length 1024 FFT, this means enumerating 496 indices less than half the total.
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