scipy.signal.check_NOLA#
- scipy.signal.check_NOLA(window, nperseg, noverlap, tol=1e-10)[source]#
Check whether the Nonzero Overlap Add (NOLA) constraint is met.
- Parameters:
- windowstr 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. Seeget_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.- npersegint
Length of each segment.
- noverlapint
Number of points to overlap between segments.
- tolfloat, optional
The allowed variance of a bin’s weighted sum from the median bin sum.
- Returns:
- verdictbool
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):\[\sum_{t}w^{2}[n-tH] \ne 0\]for all \(n\), where \(w\) is the window function, \(t\) is the frame index, and \(H\) is the hop size (\(H\) = 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.
New in version 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