; the default is False. See :func:`fft` for more details. workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from ``os.cpu_count()``. See :func:`~scipy.fft.fft` for more details. plan : object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy. .. versionadded:: 1.5.0 Returns ------- out : complex ndarray The truncated or zero-padded input, transformed along the axes indicated by `axes`, or by a combination of `s` and `x`, as explained in the parameters section above. Raises ------ ValueError If `s` and `axes` have different length. IndexError If an element of `axes` is larger than the number of axes of `x`. See Also -------- ifftn : The inverse of `fftn`, the inverse N-D FFT. fft : The 1-D FFT, with definitions and conventions used. rfftn : The N-D FFT of real input. fft2 : The 2-D FFT. fftshift : Shifts zero-frequency terms to centre of array. Notes ----- The output, analogously to `fft`, contains the term for zero frequency in the low-order corner of all axes, the positive frequency terms in the first half of all axes, the term for the Nyquist frequency in the middle of all axes and the negative frequency terms in the second half of all axes, in order of decreasingly negative frequency. Examples -------- >>> import scipy.fft >>> import numpy as np >>> x = np.mgrid[:3, :3, :3][0] >>> scipy.fft.fftn(x, axes=(1, 2)) array([[[ 0.+0.j, 0.+0.j, 0.+0.j], # may vary [ 0.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j]], [[ 9.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j]], [[18.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j]]]) >>> scipy.fft.fftn(x, (2, 2), axes=(0, 1)) array([[[ 2.+0.j, 2.+0.j, 2.+0.j], # may vary [ 0.+0.j, 0.+0.j, 0.+0.j]], [[-2.+0.j, -2.+0.j, -2.+0.j], [ 0.+0.j, 0.+0.j, 0.+0.j]]]) >>> import matplotlib.pyplot as plt >>> rng = np.random.default_rng() >>> [X, Y] = np.meshgrid(2 * np.pi * np.arange(200) / 12, ... 2 * np.pi * np.arange(200) / 34) >>> S = np.sin(X) + np.cos(Y) + rng.uniform(0, 1, X.shape) >>> FS = scipy.fft.fftn(S) >>> plt.imshow(np.log(np.abs(scipy.fft.fftshift(FS))**2)) >>> plt.show() r