Chris@82: Chris@82: Chris@82: Chris@82: Chris@82:
Chris@82:Chris@82: Previous: Real-to-Real Transforms, Up: Basic Interface [Contents][Index]
Chris@82:FFTW currently supports 11 different r2r transform kinds, specified by Chris@82: one of the constants below. For the precise definitions of these Chris@82: transforms, see What FFTW Really Computes. For a more colloquial Chris@82: introduction to these transform kinds, see More DFTs of Real Data. Chris@82:
Chris@82:For dimension of size n
, there is a corresponding “logical”
Chris@82: dimension N
that determines the normalization (and the optimal
Chris@82: factorization); the formula for N
is given for each kind below.
Chris@82: Also, with each transform kind is listed its corrsponding inverse
Chris@82: transform. FFTW computes unnormalized transforms: a transform followed
Chris@82: by its inverse will result in the original data multiplied by N
Chris@82: (or the product of the N
’s for each dimension, in
Chris@82: multi-dimensions).
Chris@82:
Chris@82:
FFTW_R2HC
computes a real-input DFT with output in
Chris@82: “halfcomplex” format, i.e. real and imaginary parts for a transform of
Chris@82: size n
stored as:
Chris@82: Chris@82: r0, r1, r2, ..., rn/2, i(n+1)/2-1, ..., i2, i1 Chris@82:
Chris@82: (LogicalN=n
, inverse is FFTW_HC2R
.)
Chris@82:
Chris@82: FFTW_HC2R
computes the reverse of FFTW_R2HC
, above.
Chris@82: (Logical N=n
, inverse is FFTW_R2HC
.)
Chris@82:
Chris@82: FFTW_DHT
computes a discrete Hartley transform.
Chris@82: (Logical N=n
, inverse is FFTW_DHT
.)
Chris@82:
Chris@82:
Chris@82: FFTW_REDFT00
computes an REDFT00 transform, i.e. a DCT-I.
Chris@82: (Logical N=2*(n-1)
, inverse is FFTW_REDFT00
.)
Chris@82:
Chris@82:
Chris@82:
Chris@82: FFTW_REDFT10
computes an REDFT10 transform, i.e. a DCT-II (sometimes called “the” DCT).
Chris@82: (Logical N=2*n
, inverse is FFTW_REDFT01
.)
Chris@82:
Chris@82: FFTW_REDFT01
computes an REDFT01 transform, i.e. a DCT-III (sometimes called “the” IDCT, being the inverse of DCT-II).
Chris@82: (Logical N=2*n
, inverse is FFTW_REDFT=10
.)
Chris@82:
Chris@82:
Chris@82: FFTW_REDFT11
computes an REDFT11 transform, i.e. a DCT-IV.
Chris@82: (Logical N=2*n
, inverse is FFTW_REDFT11
.)
Chris@82:
Chris@82: FFTW_RODFT00
computes an RODFT00 transform, i.e. a DST-I.
Chris@82: (Logical N=2*(n+1)
, inverse is FFTW_RODFT00
.)
Chris@82:
Chris@82:
Chris@82:
Chris@82: FFTW_RODFT10
computes an RODFT10 transform, i.e. a DST-II.
Chris@82: (Logical N=2*n
, inverse is FFTW_RODFT01
.)
Chris@82:
Chris@82: FFTW_RODFT01
computes an RODFT01 transform, i.e. a DST-III.
Chris@82: (Logical N=2*n
, inverse is FFTW_RODFT=10
.)
Chris@82:
Chris@82: FFTW_RODFT11
computes an RODFT11 transform, i.e. a DST-IV.
Chris@82: (Logical N=2*n
, inverse is FFTW_RODFT11
.)
Chris@82:
Chris@82: Chris@82: Previous: Real-to-Real Transforms, Up: Basic Interface [Contents][Index]
Chris@82: