MATLAB Function Reference  ifftn

Multidimensional inverse discrete Fourier transform

Syntax

• ```Y = ifftn(X)
Y = ifftn(X`,`siz)
y = ifftn(..., 'nonsymmetric')
y = ifftn(..., 'nonsymmetric')
```

Description

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

`ifftn` tests `X` to see whether it is conjugate symmetric. If so, the computation is faster and the output is real. An `N1`-by-`N2`-by- ... `Nk` array `X` is conjugate symmetric if

• ```X(i1,i2, ...,ik) = conj(X(mod(N1-i1+1,N1)+1, mod(N2-i2+1,N2)+1,
... mod(Nk-ik+1,Nk)+1))
```

for each element of `X`.

```Y = ifftn(X,siz) ``` pads `X` with zeros, or truncates `X`, to create a multidimensional array of size `siz` before performing the inverse transform. The size of the result `Y` is `siz`.

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

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

Remarks

For any `X`, `ifftn(fftn(X))` equals `X` within roundoff error.

Algorithm

`ifftn(X)` is equivalent to

• ```Y = X;
for p = 1:length(size(X))
Y = ifft(Y,[],p);
end
```

This computes in-place the one-dimensional inverse DFT along each dimension of `X`.

The execution time for i`fftn` 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 `ifftn` 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

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

See Also

`fftn`, `fftw`, `ifft`, `ifft2`, i`fftshift`

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