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4.3.6 Real-to-Real Transform Kinds

FFTW currently supports 11 different r2r transform kinds, specified by one of the constants below. For the precise definitions of these transforms, see What FFTW Really Computes. For a more colloquial introduction to these transform kinds, see More DFTs of Real Data.

For dimension of size n, there is a corresponding “logical” dimension N that determines the normalization (and the optimal factorization); the formula for N is given for each kind below. Also, with each transform kind is listed its corrsponding inverse transform. FFTW computes unnormalized transforms: a transform followed by its inverse will result in the original data multiplied by N (or the product of the N's for each dimension, in multi-dimensions).