MATLAB Function Reference 
Inverse discrete Fourier transform
Syntax
y = ifft(X) y = ifft(X,n) y = ifft(X,[],dim) y = ifft(X,n,dim)y = ifft(..., 'symmetric')
y = ifft(..., 'nonsymmetric')
Description
y = ifft(X)
returns the inverse discrete Fourier transform (DFT) of vector X
, computed with a fast Fourier transform (FFT) algorithm. If X
is a matrix, ifft
returns the inverse DFT of each column of the matrix.
ifft
tests X
to see whether vectors in X
along the active dimension are conjugate symmetric. If so, the computation is faster and the output is real. An N
element vector x
is conjugate symmetric if x(i) = conj(x(mod(Ni+1,N)+1))
for each element of x
.
If X
is a multidimensional array, ifft
operates on the first nonsingleton dimension.
y = ifft(X,n)
returns the n
point inverse DFT of vector X
.
y = ifft(X,[],dim)
and y = ifft(X,n,dim)
return the inverse DFT of X
across the dimension dim
.
y = ifft(..., 'symmetric')
causes ifft
to treat X
as conjugate symmetric along the active dimension. This option is useful when X
is not exactly conjugate symmetric, merely because of roundoff error.
y = ifft(..., 'nonsymmetric')
is the same as calling ifft(...)
without the argument 'nonsymmetric'
.
For any X
, ifft(fft(X))
equals X
to within roundoff error.
Algorithm
The algorithm for ifft(X)
is the same as the algorithm for fft(X)
, except for a sign change and a scale factor of n
=
length(X)
. As for fft
, the execution time for ifft
depends on the length of the transform. It is fastest for powers of two. It is almost as fast for lengths that have only small prime factors. It is typically several times slower for lengths that are prime or which have large prime factors.
Note
You might be able to increase the speed of ifft using the utility function fftw , which controls how MATLAB optimizes the algorithm used to compute an FFT of a particular size and dimension.

Data Type Support
ifft
supports inputs of data types double
and single
. If you call ifft
with the syntax y = ifft(X, ...)
, the output y
has the same data type as the input X
.
See Also
fft
, fft2
, ifft2
, ifftn
, ifftshift
, fftw
, ifft2
, ifftn
dftmtx
and freqz
, in the Signal Processing Toolbox
if  ifft2 
© 19942005 The MathWorks, Inc.