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# ifft2

2-D inverse fast Fourier transform

## Syntax

Y = ifft2(X)
Y = ifft2(X,m,n)
y = ifft2(..., 'symmetric')
y = ifft2(..., 'nonsymmetric')

## Description

Y = ifft2(X) returns the two-dimensional inverse discrete Fourier transform (DFT) of X, computed with a fast Fourier transform (FFT) algorithm. The result Y is the same size as X.

ifft2 tests X to see whether it is conjugate symmetric. If so, the computation is faster and the output is real. An M-by-N matrix X is conjugate symmetric if X(i,j) = conj(X(mod(M-i+1, M) + 1, mod(N-j+1, N) + 1)) for each element of X.

Y = ifft2(X,m,n) returns the m-by-n inverse fast Fourier transform of matrix X.

y = ifft2(..., 'symmetric') causes ifft2 to treat X as conjugate symmetric. This option is useful when X is not exactly conjugate symmetric, merely because of round-off error.

y = ifft2(..., 'nonsymmetric') is the same as calling ifft2(...) without the argument 'nonsymmetric'.

For any X, ifft2(fft2(X)) equals X to within roundoff error.

## Data Type Support

ifft2 supports inputs of data types double and single. If you call ifft2 with the syntax y = ifft2(X, ...), the output y has the same data type as the input X.

## More About

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### Algorithms

The algorithm for ifft2(X) is the same as the algorithm for fft2(X), except for a sign change and scale factors of [m,n] = size(X). The execution time for ifft2 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 ifft2 using the utility function fftw, which controls how MATLAB® software optimizes the algorithm used to compute an FFT of a particular size and dimension.

## See Also

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