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

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):

$$\sum_{t}w^{2}[n-tH] \ne 0$$

for all $n$ , where $w$ is the window function, $t$ is the frame index, and $H$ is the hop size ( $H$ = :None:None:`nperseg` - :None:None:`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

Parameters

window : str or tuple or array_like: Desired window to use. If :None:None:`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 :None:None:`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: :None:None:`True` if chosen combination satisfies the NOLA constraint within :None:None:`tol`, :None:None:`False` otherwise

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

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

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.signal._spectral_py.check_NOLA scipy.signal._spectral_py.stft scipy.signal._spectral_py.check_COLA scipy.signal._spectral_py.istft

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