Real-to-Real Transform Kinds

d@0: d@0: d@0: Real-to-Real Transform Kinds - FFTW 3.2.1 d@0: d@0: d@0: d@0: d@0: d@0: d@0: d@0: d@0: d@0: d@0: d@0: d@0:

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4.3.6 Real-to-Real Transform Kinds

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d@0: FFTW currently supports 11 different r2r transform kinds, specified by d@0: one of the constants below. For the precise definitions of these d@0: transforms, see What FFTW Really Computes. For a more colloquial d@0: introduction to these transform kinds, see More DFTs of Real Data. d@0: d@0:

For dimension of size n, there is a corresponding “logical” d@0: dimension N that determines the normalization (and the optimal d@0: factorization); the formula for N is given for each kind below. d@0: Also, with each transform kind is listed its corrsponding inverse d@0: transform. FFTW computes unnormalized transforms: a transform followed d@0: by its inverse will result in the original data multiplied by N d@0: (or the product of the N's for each dimension, in d@0: multi-dimensions). d@0: d@0:

FFTW_R2HC computes a real-input DFT with output in d@0: “halfcomplex” format, i.e. real and imaginary parts for a transform of d@0: size n stored as: d@0:
d@0: r₀, r₁, r₂, ..., r_n/2, i_(n+1)/2-1, ..., i₂, i₁ d@0:
(Logical N=n, inverse is FFTW_HC2R.) d@0: d@0:
FFTW_HC2R computes the reverse of FFTW_R2HC, above. d@0: (Logical N=n, inverse is FFTW_R2HC.) d@0: d@0:
FFTW_DHT computes a discrete Hartley transform. d@0: (Logical N=n, inverse is FFTW_DHT.) d@0: d@0:
FFTW_REDFT00 computes an REDFT00 transform, i.e. a DCT-I. d@0: (Logical N=2*(n-1), inverse is FFTW_REDFT00.) d@0: d@0:
FFTW_REDFT10 computes an REDFT10 transform, i.e. a DCT-II (sometimes called “the” DCT). d@0: (Logical N=2*n, inverse is FFTW_REDFT01.) d@0: d@0:
FFTW_REDFT01 computes an REDFT01 transform, i.e. a DCT-III (sometimes called “the” IDCT, being the inverse of DCT-II). d@0: (Logical N=2*n, inverse is FFTW_REDFT=10.) d@0: d@0:
FFTW_REDFT11 computes an REDFT11 transform, i.e. a DCT-IV. d@0: (Logical N=2*n, inverse is FFTW_REDFT11.) d@0: d@0:
FFTW_RODFT00 computes an RODFT00 transform, i.e. a DST-I. d@0: (Logical N=2*(n+1), inverse is FFTW_RODFT00.) d@0: d@0:
FFTW_RODFT10 computes an RODFT10 transform, i.e. a DST-II. d@0: (Logical N=2*n, inverse is FFTW_RODFT01.) d@0: d@0:
FFTW_RODFT01 computes an RODFT01 transform, i.e. a DST-III. d@0: (Logical N=2*n, inverse is FFTW_RODFT=10.) d@0: d@0:
FFTW_RODFT11 computes an RODFT11 transform, i.e. a DST-IV. d@0: (Logical N=2*n, inverse is FFTW_RODFT11.) d@0: d@0:

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