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Module « numpy.fft »

Fonction ifft - module numpy.fft

Signature de la fonction ifft

def ifft(a, n=None, axis=-1, norm=None, out=None) 

Description

help(numpy.fft.ifft)

Compute the one-dimensional inverse discrete Fourier Transform.

This function computes the inverse of the one-dimensional *n*-point
discrete Fourier transform computed by `fft`.  In other words,
``ifft(fft(a)) == a`` to within numerical accuracy.
For a general description of the algorithm and definitions,
see `numpy.fft`.

The input should be ordered in the same way as is returned by `fft`,
i.e.,

* ``a[0]`` should contain the zero frequency term,
* ``a[1:n//2]`` should contain the positive-frequency terms,
* ``a[n//2 + 1:]`` should contain the negative-frequency terms, in
  increasing order starting from the most negative frequency.

For an even number of input points, ``A[n//2]`` represents the sum of
the values at the positive and negative Nyquist frequencies, as the two
are aliased together. See `numpy.fft` for details.

Parameters
----------
a : array_like
    Input array, can be complex.
n : int, optional
    Length of the transformed axis of the output.
    If `n` is smaller than the length of the input, the input is cropped.
    If it is larger, the input is padded with zeros.  If `n` is not given,
    the length of the input along the axis specified by `axis` is used.
    See notes about padding issues.
axis : int, optional
    Axis over which to compute the inverse DFT.  If not given, the last
    axis is used.
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.

    .. versionadded:: 2.0.0

Returns
-------
out : complex ndarray
    The truncated or zero-padded input, transformed along the axis
    indicated by `axis`, or the last one if `axis` is not specified.

Raises
------
IndexError
    If `axis` is not a valid axis of `a`.

See Also
--------
numpy.fft : An introduction, with definitions and general explanations.
fft : The one-dimensional (forward) FFT, of which `ifft` is the inverse
ifft2 : The two-dimensional inverse FFT.
ifftn : The n-dimensional inverse FFT.

Notes
-----
If the input parameter `n` is larger than the size of the input, the input
is padded by appending zeros at the end.  Even though this is the common
approach, it might lead to surprising results.  If a different padding is
desired, it must be performed before calling `ifft`.

Examples
--------
>>> import numpy as np
>>> np.fft.ifft([0, 4, 0, 0])
array([ 1.+0.j,  0.+1.j, -1.+0.j,  0.-1.j]) # may vary

Create and plot a band-limited signal with random phases:

>>> import matplotlib.pyplot as plt
>>> t = np.arange(400)
>>> n = np.zeros((400,), dtype=complex)
>>> n[40:60] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20,)))
>>> s = np.fft.ifft(n)
>>> plt.plot(t, s.real, label='real')
[<matplotlib.lines.Line2D object at ...>]
>>> plt.plot(t, s.imag, '--', label='imaginary')
[<matplotlib.lines.Line2D object at ...>]
>>> plt.legend()
<matplotlib.legend.Legend object at ...>
>>> plt.show()

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