# ifft

Inverse fast Fourier transform

## Description

`X = ifft(`

computes
the inverse discrete Fourier transform of `Y`

)`Y`

using
a fast Fourier transform algorithm. `X`

is the same
size as `Y`

.

If

`Y`

is a vector, then`ifft(Y)`

returns the inverse transform of the vector.If

`Y`

is a matrix, then`ifft(Y)`

returns the inverse transform of each column of the matrix.If

`Y`

is a multidimensional array, then`ifft(Y)`

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

## Examples

## Input Arguments

## More About

## Algorithms

The

`ifft`

function tests whether the vectors in`Y`

are conjugate symmetric. If the vectors in`Y`

are conjugate symmetric, then the inverse transform computation is faster and the output is real.A function $$g(a)$$ is conjugate symmetric if $$g(a)={g}^{*}(-a)$$. However, the fast Fourier transform of a time-domain signal has one half of its spectrum in positive frequencies and the other half in negative frequencies, with the first element reserved for the zero frequency. For this reason, a vector

`v`

is conjugate symmetric when`v(2:end)`

is equal to`conj(v(end:-1:2))`

.

## Extended Capabilities

## Version History

**Introduced before R2006a**