Module « numpy.fft »

Fonction hfft - module numpy.fft

Signature de la fonction hfft

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

Description

hfft.__doc__

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

    Parameters
    ----------
    a : 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
        .. versionadded:: 1.10.0

        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.

    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 one-dimensional FFT for real input.
    ihfft : The inverse of `hfft`.

    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.

    The correct interpretation of the hermitian input depends on the length of
    the original data, as given by `n`. This is because each input shape could
    correspond to either an odd or even length signal. By default, `hfft`
    assumes an even output length which puts the last entry at the Nyquist
    frequency; aliasing with its symmetric counterpart. By Hermitian symmetry,
    the value is thus treated as purely real. To avoid losing information, the
    shape of the full signal **must** be given.

    Examples
    --------
    >>> signal = np.array([1, 2, 3, 4, 3, 2])
    >>> np.fft.fft(signal)
    array([15.+0.j,  -4.+0.j,   0.+0.j,  -1.-0.j,   0.+0.j,  -4.+0.j]) # may vary
    >>> np.fft.hfft(signal[:4]) # Input first half of signal
    array([15.,  -4.,   0.,  -1.,   0.,  -4.])
    >>> np.fft.hfft(signal, 6)  # Input entire signal and truncate
    array([15.,  -4.,   0.,  -1.,   0.,  -4.])


    >>> signal = np.array([[1, 1.j], [-1.j, 2]])
    >>> np.conj(signal.T) - signal   # check Hermitian symmetry
    array([[ 0.-0.j,  -0.+0.j], # may vary
           [ 0.+0.j,  0.-0.j]])
    >>> freq_spectrum = np.fft.hfft(signal)
    >>> freq_spectrum
    array([[ 1.,  1.],
           [ 2., -2.]])