Inverse and other FFT Transforms
f can be reconstructed from its discrete Fourier transformation G(f) by
f = ?*. G(f)/N where * denotes complex conjugation
- ?* is an N by N matrix and G(f) is a vector of length N
Most applications require both calculating FFT’s and reconstructing functions from their FFT’s
- However these are essentially the same algorithm as seen above and so we only need to illustrate one case
- Issues with parallelism and optimal performance are identical
For solving the Poisson equation and various other applications, we use variations on the FFT
- The sin transform – use imaginary part of G
- The cos transform – use real part of G