# Forward domain of transform

As already mentioned in the introduction to the Fourier Transform Functions section, the general form of the discrete Fourier transform is

for `k1 = 0,±1,±2, ... ,` where σ is an arbitrary real-valued scale factor and `δ = ±1`. The forward transform is defined by `σ = 1` and `δ = -1`. In most common situations, the domain of the forward transform, that is, the set where the input (periodic) sequence `{wj1, j2, ..., jd}` belongs, can be either the set of complex-valued sequences, real-valued sequences, and complex-valued conjugate even sequences. The configuration parameter `DFTI_FORWARD_DOMAIN` indicates the domain for the forward transform. Note that this implicitly specifies the domain for the backward transform because of mathematical property of the FFT. See Table “Correspondence of Forward and Backward Domain” for details.

Correspondence of Forward and Backward Domain
Forward Domain | Implied Backward Domain
--- | ---
Complex | `(DFTI_COMPLEX)` | Complex
Real | `(DFTI_REAL)` | Conjugate Even

On transforms in the real domain, some software packages only offer one "real-to-complex" transform. This in essence omits the conjugate even domain for the forward transform. The forward domain configuration parameter `DFTI_FORWARD_DOMAIN` is the second of four configuration parameters without default value.

Parent topic: Configuration Settings