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Module « scipy.fft »

Fonction ifft - module scipy.fft

Signature de la fonction ifft

def ifft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *, plan=None) 

Description

help(scipy.fft.ifft)

Compute the 1-D inverse discrete Fourier Transform.

This function computes the inverse of the 1-D *n*-point
discrete Fourier transform computed by `fft`.  In other words,
``ifft(fft(x)) == x`` to within numerical accuracy.

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

* ``x[0]`` should contain the zero frequency term,
* ``x[1:n//2]`` should contain the positive-frequency terms,
* ``x[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, ``x[n//2]`` represents the sum of
the values at the positive and negative Nyquist frequencies, as the two
are aliased together. See `fft` for details.

Parameters
----------
x : 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 `fft`). Default is "backward".
overwrite_x : bool, optional
    If True, the contents of `x` can be destroyed; 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 axis
    indicated by `axis`, or the last one if `axis` is not specified.

Raises
------
IndexError
    If `axes` is larger than the last axis of `x`.

See Also
--------
fft : The 1-D (forward) FFT, of which `ifft` is the inverse.
ifft2 : The 2-D inverse FFT.
ifftn : The N-D 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`.

If ``x`` is a 1-D array, then the `ifft` is equivalent to ::

    y[k] = np.sum(x * np.exp(2j * np.pi * k * np.arange(n)/n)) / len(x)

As with `fft`, `ifft` has support for all floating point types and is
optimized for real input.

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

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