DFTI_FORWARD_DOMAIN

The general form of a discrete Fourier transform is

where w is the input sequence, z is the output sequence, both indexed by k_l = 0, ... n_l-1, for l = 1, ..., d, scale factor σ is an arbitrary real number with the default value of 1.0, δ is the sign in the exponent, and δ = -1 for the forward transform and δ = +1 for the backward transform.

The Intel MKL implementation of the FFT algorithm, used for fast computation of discrete Fourier transforms, supports forward transforms on input sequences of two domains, as specified by configuration parameter DFTI_FORWARD_DOMAIN: general complex-valued sequences (DFTI_COMPLEX domain) and general real-valued sequences (DFTI_REAL domain). The forward transform maps the forward domain to the corresponding backward domain, as shown in Table "Correspondence of Forward and Backward Domain".

The conjugate-even domain covers complex-valued sequences with the symmetry property:

where the index arithmetic is performed modulo respective size, that is,

and therefore

Due to this property of conjugate-even sequences, only a part of such sequence is stored in the computer memory, as described in DFTI_CONJUGATE_EVEN_STORAGE.

DFTI_FORWARD_DOMAIN does not have a default value. Set it explicitly by calling the DftiCreateDescriptor function.