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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:
r_{0}, r_{1}, r_{2}, ..., r_{n/2}, i_{(n+1)/2-1}, ..., i_{2}, i_{1}
(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
.)
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