Module « scipy.signal »

Fonction check_NOLA - module scipy.signal

Signature de la fonction check_NOLA

def check_NOLA(window, nperseg, noverlap, tol=1e-10) 

Description

check_NOLA.__doc__

Check whether the Nonzero Overlap Add (NOLA) constraint is met.

    Parameters
    ----------
    window : str or tuple or array_like
        Desired window to use. If `window` is a string or tuple, it is
        passed to `get_window` to generate the window values, which are
        DFT-even by default. See `get_window` for a list of windows and
        required parameters. If `window` is array_like it will be used
        directly as the window and its length must be nperseg.
    nperseg : int
        Length of each segment.
    noverlap : int
        Number of points to overlap between segments.
    tol : float, optional
        The allowed variance of a bin's weighted sum from the median bin
        sum.

    Returns
    -------
    verdict : bool
        `True` if chosen combination satisfies the NOLA constraint within
        `tol`, `False` otherwise

    See Also
    --------
    check_COLA: Check whether the Constant OverLap Add (COLA) constraint is met
    stft: Short Time Fourier Transform
    istft: Inverse Short Time Fourier Transform

    Notes
    -----
    In order to enable inversion of an STFT via the inverse STFT in
    `istft`, the signal windowing must obey the constraint of "nonzero
    overlap add" (NOLA):

    .. math:: \sum_{t}w^{2}[n-tH] \ne 0

    for all :math:`n`, where :math:`w` is the window function, :math:`t` is the
    frame index, and :math:`H` is the hop size (:math:`H` = `nperseg` -
    `noverlap`).

    This ensures that the normalization factors in the denominator of the
    overlap-add inversion equation are not zero. Only very pathological windows
    will fail the NOLA constraint.

    .. versionadded:: 1.2.0

    References
    ----------
    .. [1] Julius O. Smith III, "Spectral Audio Signal Processing", W3K
           Publishing, 2011,ISBN 978-0-9745607-3-1.
    .. [2] G. Heinzel, A. Ruediger and R. Schilling, "Spectrum and
           spectral density estimation by the Discrete Fourier transform
           (DFT), including a comprehensive list of window functions and
           some new at-top windows", 2002,
           http://hdl.handle.net/11858/00-001M-0000-0013-557A-5

    Examples
    --------
    >>> from scipy import signal

    Confirm NOLA condition for rectangular window of 75% (3/4) overlap:

    >>> signal.check_NOLA(signal.windows.boxcar(100), 100, 75)
    True

    NOLA is also true for 25% (1/4) overlap:

    >>> signal.check_NOLA(signal.windows.boxcar(100), 100, 25)
    True

    "Symmetrical" Hann window (for filter design) is also NOLA:

    >>> signal.check_NOLA(signal.windows.hann(120, sym=True), 120, 60)
    True

    As long as there is overlap, it takes quite a pathological window to fail
    NOLA:

    >>> w = np.ones(64, dtype="float")
    >>> w[::2] = 0
    >>> signal.check_NOLA(w, 64, 32)
    False

    If there is not enough overlap, a window with zeros at the ends will not
    work:

    >>> signal.check_NOLA(signal.windows.hann(64), 64, 0)
    False
    >>> signal.check_NOLA(signal.windows.hann(64), 64, 1)
    False
    >>> signal.check_NOLA(signal.windows.hann(64), 64, 2)
    True