| 1 |
f can be reconstructed from its discrete Fourier transformation G(f) by
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| 2 |
f = ?*. G(f)/N where * denotes complex conjugation
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?* is an N by N matrix and G(f) is a vector of length N
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| 3 |
Most applications require both calculating FFT's and reconstructing functions from their FFT's
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However these are essentially the same algorithm as seen above and so we only need to illustrate one case
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Issues with parallelism and optimal performance are identical
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| 4 |
For solving the Poisson equation and various other applications, we use variations on the FFT
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The sin transform – use imaginary part of G
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The cos transform – use real part of G
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