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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

help(scipy.signal.check_NOLA)

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
--------
>>> import numpy as np
>>> 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

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