numpy.fft.ifftn¶

numpy.fft.
ifftn
(a, s=None, axes=None, norm=None)[source]¶ Compute the Ndimensional inverse discrete Fourier Transform.
This function computes the inverse of the Ndimensional discrete Fourier Transform over any number of axes in an Mdimensional array by means of the Fast Fourier Transform (FFT). In other words,
ifftn(fftn(a)) == a
to within numerical accuracy. For a description of the definitions and conventions used, seenumpy.fft
.The input, analogously to
ifft
, should be ordered in the same way as is returned byfftn
, i.e. it should have the term for zero frequency in all axes in the loworder corner, 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.Parameters: a : array_like
Input array, can be complex.
s : sequence of ints, optional
Shape (length of each transformed axis) of the output (
s[0]
refers to axis 0,s[1]
to axis 1, etc.). This corresponds ton
forifft(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. if s is not given, the shape of the input along the axes specified by axes is used. See notes for issue onifft
zero padding.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.norm : {None, “ortho”}, optional
New in version 1.10.0.
Normalization mode (see
numpy.fft
). Default is None.Returns: out : complex ndarray
The truncated or zeropadded 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 ndimensional FFT, of which
ifftn
is the inverse. ifft
 The onedimensional inverse FFT.
ifft2
 The twodimensional inverse FFT.
ifftshift
 Undoes
fftshift
, shifts zerofrequency terms to beginning of array.
Notes
See
numpy.fft
for definitions and conventions used.Zeropadding, 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 beforeifftn
is called.Examples
>>> 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], [ 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 bandlimited 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) <matplotlib.image.AxesImage object at 0x...> >>> plt.show()
(Source code, png, pdf)