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Module « numpy.fft »

Fonction ifftn - module numpy.fft

Signature de la fonction ifftn

def ifftn(a, s=None, axes=None, norm=None, out=None) 

Description

help(numpy.fft.ifftn)

Compute the N-dimensional inverse discrete Fourier Transform.

This function computes the inverse of the N-dimensional discrete
Fourier Transform over any number of axes in an M-dimensional 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, see `numpy.fft`.

The input, analogously to `ifft`, should be ordered in the same way as is
returned by `fftn`, i.e. it should have the term for zero frequency
in all axes in the low-order 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 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)
<matplotlib.image.AxesImage object at 0x...>
>>> plt.show()

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