Chris@19: Previous: Real-to-Real Transforms, Chris@19: Up: Basic Interface Chris@19:
Chris@19: FFTW currently supports 11 different r2r transform kinds, specified by Chris@19: one of the constants below. For the precise definitions of these Chris@19: transforms, see What FFTW Really Computes. For a more colloquial Chris@19: introduction to these transform kinds, see More DFTs of Real Data. Chris@19: Chris@19:
For dimension of size n, there is a corresponding “logical”
Chris@19: dimension N that determines the normalization (and the optimal
Chris@19: factorization); the formula for N is given for each kind below.
Chris@19: Also, with each transform kind is listed its corrsponding inverse
Chris@19: transform. FFTW computes unnormalized transforms: a transform followed
Chris@19: by its inverse will result in the original data multiplied by N
Chris@19: (or the product of the N's for each dimension, in
Chris@19: multi-dimensions).
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FFTW_R2HC computes a real-input DFT with output in
Chris@19: “halfcomplex” format, i.e. real and imaginary parts for a transform of
Chris@19: size n stored as:
Chris@19: Chris@19: r0, r1, r2, ..., rn/2, i(n+1)/2-1, ..., i2, i1 Chris@19:
(LogicalN=n, inverse is FFTW_HC2R.)
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Chris@19: FFTW_HC2R computes the reverse of FFTW_R2HC, above.
Chris@19: (Logical N=n, inverse is FFTW_R2HC.)
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Chris@19: FFTW_DHT computes a discrete Hartley transform.
Chris@19: (Logical N=n, inverse is FFTW_DHT.)
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Chris@19: FFTW_REDFT00 computes an REDFT00 transform, i.e. a DCT-I.
Chris@19: (Logical N=2*(n-1), inverse is FFTW_REDFT00.)
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Chris@19: FFTW_REDFT10 computes an REDFT10 transform, i.e. a DCT-II (sometimes called “the” DCT).
Chris@19: (Logical N=2*n, inverse is FFTW_REDFT01.)
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Chris@19: FFTW_REDFT01 computes an REDFT01 transform, i.e. a DCT-III (sometimes called “the” IDCT, being the inverse of DCT-II).
Chris@19: (Logical N=2*n, inverse is FFTW_REDFT=10.)
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Chris@19: FFTW_REDFT11 computes an REDFT11 transform, i.e. a DCT-IV.
Chris@19: (Logical N=2*n, inverse is FFTW_REDFT11.)
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Chris@19: FFTW_RODFT00 computes an RODFT00 transform, i.e. a DST-I.
Chris@19: (Logical N=2*(n+1), inverse is FFTW_RODFT00.)
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Chris@19: FFTW_RODFT10 computes an RODFT10 transform, i.e. a DST-II.
Chris@19: (Logical N=2*n, inverse is FFTW_RODFT01.)
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Chris@19: FFTW_RODFT01 computes an RODFT01 transform, i.e. a DST-III.
Chris@19: (Logical N=2*n, inverse is FFTW_RODFT=10.)
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Chris@19: FFTW_RODFT11 computes an RODFT11 transform, i.e. a DST-IV.
Chris@19: (Logical N=2*n, inverse is FFTW_RODFT11.)
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