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- numpy.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. 
 
 - See also - Notes - If - xis 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 - >>> import numpy as np >>> from scipy.fftpack import fftn, ifftn >>> y = (-np.arange(16), 8 - np.arange(16), np.arange(16)) >>> np.allclose(y, fftn(ifftn(y))) True