xis 0, ``s[1]`` to axis 1, etc.). This corresponds to ``n`` for ``ifft(x, n)``. Along any axis, if the given shape is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. .. versionchanged:: 2.0 If it is ``-1``, the whole input is used (no padding/trimming). If `s` is not given, the shape of the input along the axes specified by `axes` is used. See notes for issue on `ifft` zero padding. .. deprecated:: 2.0 If `s` is not ``None``, `axes` must not be ``None`` either. .. deprecated:: 2.0 `s` must contain only ``int`` s, not ``None`` values. ``None`` values currently mean that the default value for ``n`` is used in the corresponding 1-D transform, but this behaviour is deprecated. axes : sequence of ints, optional Axes over which to compute the IFFT. If not given, the last ``len(s)`` axes are used, or all axes if `s` is also not specified. Repeated indices in `axes` means that the inverse transform over that axis is performed multiple times. .. deprecated:: 2.0 If `s` is specified, the corresponding `axes` to be transformed must be explicitly specified too. norm : {"backward", "ortho", "forward"}, optional Normalization mode (see `numpy.fft`). Default is "backward". Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor. .. versionadded:: 1.20.0 The "backward", "forward" values were added. out : complex ndarray, optional If provided, the result will be placed in this array. It should be of the appropriate shape and dtype for all axes (and hence is incompatible with passing in all but the trivial ``s``). .. versionadded:: 2.0.0 Returns ------- out : complex ndarray The truncated or zero-padded input, transformed along the axes indicated by `axes`, or by a combination of `s` or `a`, 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 than the number of axes of `a`. See Also -------- numpy.fft : Overall view of discrete Fourier transforms, with definitions and conventions used. fftn : The forward *n*-dimensional FFT, of which `ifftn` is the inverse. ifft : The one-dimensional inverse FFT. ifft2 : The two-dimensional inverse FFT. ifftshift : Undoes `fftshift`, shifts zero-frequency terms to beginning of array. Notes ----- See `numpy.fft` for definitions and conventions used. Zero-padding, analogously with `ifft`, is performed by appending zeros to the input along the specified dimension. Although this is the common approach, it might lead to surprising results. If another form of zero padding is desired, it must be performed before `ifftn` is called. Examples -------- >>> import numpy as np >>> a = np.eye(4) >>> np.fft.ifftn(np.fft.fftn(a, axes=(0,)), axes=(1,)) array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], # may vary [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j], [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j], [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]]) Create and plot an image with band-limited frequency content: >>> import matplotlib.pyplot as plt >>> n = np.zeros((200,200), dtype=complex) >>> n[60:80, 20:40] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20, 20))) >>> im = np.fft.ifftn(n).real >>> plt.imshow(im) >>> plt.show() rK