Chris@42: Previous: Wisdom, Up: FFTW Reference [Contents][Index]
Chris@42:In this section, we provide precise mathematical definitions for the Chris@42: transforms that FFTW computes. These transform definitions are fairly Chris@42: standard, but some authors follow slightly different conventions for the Chris@42: normalization of the transform (the constant factor in front) and the Chris@42: sign of the complex exponent. We begin by presenting the Chris@42: one-dimensional (1d) transform definitions, and then give the Chris@42: straightforward extension to multi-dimensional transforms. Chris@42:
Chris@42:| • The 1d Discrete Fourier Transform (DFT): | Chris@42: | |
| • The 1d Real-data DFT: | Chris@42: | |
| • 1d Real-even DFTs (DCTs): | Chris@42: | |
| • 1d Real-odd DFTs (DSTs): | Chris@42: | |
| • 1d Discrete Hartley Transforms (DHTs): | Chris@42: | |
| • Multi-dimensional Transforms: | Chris@42: |