`scipy.signal._spectral_py:check_NOLA`

source: /scipy/signal/_spectral_py.py :1304

Signature

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

Summary

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

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):

t \sum w^{2} [n - t H] \neq = 0

for all $n$ , where $w$ is the window function, $t$ is the frame index, and $H$ is the hop size ( $H$ = 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.

Array API Standard Support

check_NOLA has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ⛔                     ⛔                   
JAX                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

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)

✗

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

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

✗

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

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

✗

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)

✗

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)
signal.check_NOLA(signal.windows.hann(64), 64, 1)
signal.check_NOLA(signal.windows.hann(64), 64, 2)

✗

Aliases

scipy.signal.check_NOLA