vendors/fftw3/doc/html/Real_002dto_002dReal-Transform-Kinds.html
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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).
FFTW_R2HC computes a real-input DFT with output in “halfcomplex” format, i.e. real and imaginary parts for a transform of size n stored as:r0, r1, r2, ..., rn/2, i(n+1)/2-1, ..., i2, i1
(Logical N=n, inverse is FFTW_HC2R.)
FFTW_HC2R computes the reverse of FFTW_R2HC, above. (Logical N=n, inverse is FFTW_R2HC.)FFTW_DHT computes a discrete Hartley transform. (Logical N=n, inverse is FFTW_DHT.)FFTW_REDFT00 computes an REDFT00 transform, i.e. a DCT-I. (Logical N=2*(n-1), inverse is FFTW_REDFT00.)FFTW_REDFT10 computes an REDFT10 transform, i.e. a DCT-II (sometimes called “the” DCT). (Logical N=2*n, inverse is FFTW_REDFT01.)FFTW_REDFT01 computes an REDFT01 transform, i.e. a DCT-III (sometimes called “the” IDCT, being the inverse of DCT-II). (Logical N=2*n, inverse is FFTW_REDFT=10.)FFTW_REDFT11 computes an REDFT11 transform, i.e. a DCT-IV. (Logical N=2*n, inverse is FFTW_REDFT11.)FFTW_RODFT00 computes an RODFT00 transform, i.e. a DST-I. (Logical N=2*(n+1), inverse is FFTW_RODFT00.)FFTW_RODFT10 computes an RODFT10 transform, i.e. a DST-II. (Logical N=2*n, inverse is FFTW_RODFT01.)FFTW_RODFT01 computes an RODFT01 transform, i.e. a DST-III. (Logical N=2*n, inverse is FFTW_RODFT=10.)FFTW_RODFT11 computes an RODFT11 transform, i.e. a DST-IV. (Logical N=2*n, inverse is FFTW_RODFT11.)Previous: Real-to-Real Transforms, Up: Basic Interface [Contents][Index]