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Fast Fourier transform

computes
the discrete
Fourier transform (DFT) of `Y`

= fft(`X`

)`X`

using a fast
Fourier transform (FFT) algorithm.

If

`X`

is a vector, then`fft(X)`

returns the Fourier transform of the vector.If

`X`

is a matrix, then`fft(X)`

treats the columns of`X`

as vectors and returns the Fourier transform of each column.If

`X`

is a multidimensional array, then`fft(X)`

treats the values along the first array dimension whose size does not equal 1 as vectors and returns the Fourier transform of each vector.

returns
the `Y`

= fft(`X`

,`n`

)`n`

-point DFT. If no value is specified, `Y`

is
the same size as `X`

.

If

`X`

is a vector and the length of`X`

is less than`n`

, then`X`

is padded with trailing zeros to length`n`

.If

`X`

is a vector and the length of`X`

is greater than`n`

, then`X`

is truncated to length`n`

.If

`X`

is a matrix, then each column is treated as in the vector case.If

`X`

is a multidimensional array, then the first array dimension whose size does not equal 1 is treated as in the vector case.

[1] FFTW (`http://www.fftw.org`

)

[2] Frigo, M., and S. G. Johnson. "FFTW:
An Adaptive Software Architecture for the FFT." *Proceedings
of the International Conference on Acoustics, Speech, and Signal
Processing*. Vol. 3, 1998, pp. 1381-1384.

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