Multidimensional inverse fast Fourier transform
X = ifftn(Y)
X = ifftn(Y,sz)
X = ifftn(___,symflag)
X = ifftn( returns
discrete inverse Fourier transform of an N-D array using a
fast Fourier transform algorithm. The N-D inverse transform is equivalent
to computing the 1-D inverse transform along each dimension of
X is the same size as
X = ifftn( truncates
Y with trailing zeros before taking the inverse
transform according to the elements of the vector
Each element of
sz defines the length of the corresponding
transform dimension. For example, if
Y is a 5-by-5-by-5
X = ifftn(Y,[8 8 8]) pads each dimension
with zeros, resulting in an 8-by-8-by-8 inverse transform
You can use the
ifftn function to convert multidimensional data sampled in frequency to data sampled in time or space. The
ifftn function also allows you to control the size of the transform.
Create a 3-by-3-by-3 array and compute its inverse Fourier transform.
Y = rand(3,3,3); ifftn(Y);
Pad the dimensions of
Y with trailing zeros so that the transform has size 8-by-8-by-8.
X = ifftn(Y,[8 8 8]); size(X)
ans = 8 8 8
For nearly conjugate symmetric arrays, you can compute the inverse Fourier transform faster by specifying the
'symmetric' option, which also ensures that the output is real.
Compute the 3-D inverse Fourier transform of a nearly conjugate symmetric array.
Y(:,:,1) = [1e-15*i 0; 1 0]; Y(:,:,2) = [0 1; 0 1]; X = ifftn(Y,'symmetric')
X = (:,:,1) = 0.3750 -0.1250 -0.1250 -0.1250 (:,:,2) = -0.1250 0.3750 -0.1250 -0.1250
Y— Input array
Input array, specified as a vector, a matrix, or a multidimensional
Y is of type
ifftn natively computes in single precision,
X is also of type
X is returned as type
Complex Number Support: Yes
sz— Lengths of inverse transform dimensions
Lengths of inverse transform dimensions, specified as a vector of positive integers.
symflag— Symmetry type
Symmetry type, specified as
Y is not exactly conjugate symmetric due to
if it were conjugate symmetric. For more information on conjugate
symmetry, see Algorithms.
The discrete inverse Fourier transform X of an N-D array Y is defined as
Each dimension has length mk for k = 1,2,...,N, and are complex roots of unity where i is the imaginary unit.
ifftn function tests whether
the vectors in an array
Y are conjugate symmetric
in all dimensions. A vector
v is conjugate symmetric
when the ith element satisfies
conj(v([1,end:-1:2])). If the vectors in
conjugate symmetric in all dimensions, then the inverse transform
computation is faster and the output is real.
Usage notes and limitations:
Does not support the
sz argument must have a fixed