# scipy.fftpack.fftn¶

scipy.fftpack.fftn(x, shape=None, axes=None, overwrite_x=False)[source]

Return multidimensional discrete Fourier transform.

The returned array contains:

y[j_1,..,j_d] = sum[k_1=0..n_1-1, ..., k_d=0..n_d-1]
x[k_1,..,k_d] * prod[i=1..d] exp(-sqrt(-1)*2*pi/n_i * j_i * k_i)


where d = len(x.shape) and n = x.shape.

Parameters
xarray_like

The (N-D) array to transform.

shapeint or array_like of ints or None, optional

The shape of the result. If both shape and axes (see below) are None, shape is x.shape; if shape is None but axes is not None, then shape is scipy.take(x.shape, axes, axis=0). If shape[i] > x.shape[i], the ith dimension is padded with zeros. If shape[i] < x.shape[i], the ith dimension is truncated to length shape[i]. If any element of shape is -1, the size of the corresponding dimension of x is used.

axesint or array_like of ints or None, optional

The axes of x (y if shape is not None) along which the transform is applied. The default is over all axes.

overwrite_xbool, optional

If True, the contents of x can be destroyed. Default is False.

Returns
ycomplex-valued N-D NumPy array

The (N-D) DFT of the input array.

Notes

If x is real-valued, then y[..., j_i, ...] == y[..., n_i-j_i, ...].conjugate().

Both single and double precision routines are implemented. Half precision inputs will be converted to single precision. Non-floating-point inputs will be converted to double precision. Long-double precision inputs are not supported.

Examples

>>> from scipy.fftpack import fftn, ifftn
>>> y = (-np.arange(16), 8 - np.arange(16), np.arange(16))
>>> np.allclose(y, fftn(ifftn(y)))
True


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