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Module « scipy.fft »

Fonction hfft - module scipy.fft

Signature de la fonction hfft

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

Description

help(scipy.fft.hfft)

Compute the FFT of a signal that has Hermitian symmetry, i.e., a real
spectrum.

Parameters
----------
x : array_like
    The input array.
n : int, optional
    Length of the transformed axis of the output. For `n` output
    points, ``n//2 + 1`` input points are necessary. If the input is
    longer than this, it is cropped. If it is shorter than this, it is
    padded with zeros. If `n` is not given, it is taken to be ``2*(m-1)``,
    where ``m`` is the length of the input along the axis specified by
    `axis`.
axis : int, optional
    Axis over which to compute the FFT. 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 `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 : ndarray
    The truncated or zero-padded input, transformed along the axis
    indicated by `axis`, or the last one if `axis` is not specified.
    The length of the transformed axis is `n`, or, if `n` is not given,
    ``2*m - 2``, where ``m`` is the length of the transformed axis of
    the input. To get an odd number of output points, `n` must be
    specified, for instance, as ``2*m - 1`` in the typical case,

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

See Also
--------
rfft : Compute the 1-D FFT for real input.
ihfft : The inverse of `hfft`.
hfftn : Compute the N-D FFT of a Hermitian signal.

Notes
-----
`hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the
opposite case: here the signal has Hermitian symmetry in the time
domain and is real in the frequency domain. So, here, it's `hfft`, for
which you must supply the length of the result if it is to be odd.
* even: ``ihfft(hfft(a, 2*len(a) - 2) == a``, within roundoff error,
* odd: ``ihfft(hfft(a, 2*len(a) - 1) == a``, within roundoff error.

Examples
--------
>>> from scipy.fft import fft, hfft
>>> import numpy as np
>>> a = 2 * np.pi * np.arange(10) / 10
>>> signal = np.cos(a) + 3j * np.sin(3 * a)
>>> fft(signal).round(10)
array([ -0.+0.j,   5.+0.j,  -0.+0.j,  15.-0.j,   0.+0.j,   0.+0.j,
        -0.+0.j, -15.-0.j,   0.+0.j,   5.+0.j])
>>> hfft(signal[:6]).round(10) # Input first half of signal
array([  0.,   5.,   0.,  15.,  -0.,   0.,   0., -15.,  -0.,   5.])
>>> hfft(signal, 10)  # Input entire signal and truncate
array([  0.,   5.,   0.,  15.,  -0.,   0.,   0., -15.,  -0.,   5.])

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