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cannam@167:In this section, we provide precise mathematical definitions for the cannam@167: transforms that FFTW computes. These transform definitions are fairly cannam@167: standard, but some authors follow slightly different conventions for the cannam@167: normalization of the transform (the constant factor in front) and the cannam@167: sign of the complex exponent. We begin by presenting the cannam@167: one-dimensional (1d) transform definitions, and then give the cannam@167: straightforward extension to multi-dimensional transforms. cannam@167:
cannam@167:| • The 1d Discrete Fourier Transform (DFT): | cannam@167: | |
| • The 1d Real-data DFT: | cannam@167: | |
| • 1d Real-even DFTs (DCTs): | cannam@167: | |
| • 1d Real-odd DFTs (DSTs): | cannam@167: | |
| • 1d Discrete Hartley Transforms (DHTs): | cannam@167: | |
| • Multi-dimensional Transforms: | cannam@167: |