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
(LogicalN=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.)