scipy.signal.

check_COLA#

scipy.signal.check_COLA(window, nperseg, noverlap, tol=1e-10)[source]#

Check whether the Constant OverLap Add (COLA) constraint is met (legacy function).

Legacy

This function is considered legacy and will no longer receive updates. While we currently have no plans to remove it, we recommend that new code uses more modern alternatives instead. The COLA constraint is equivalent of having a constant dual window, i.e., all(ShortTimeFFT.dual_win == ShortTimeFFT.dual_win[0]). Hence, closest_STFT_dual_window generalizes this function, as the following example shows:

>>> import numpy as np
>>> from scipy.signal import check_COLA, closest_STFT_dual_window, windows
...
>>> w, w_rect, hop = windows.hann(12, sym=False), np.ones(12), 6
>>> dual_win, alpha = closest_STFT_dual_window(w, hop, w_rect, scaled=True)
>>> np.allclose(dual_win/alpha, w_rect, atol=1e-10, rtol=0)
True
>>> check_COLA(w, len(w), len(w) - hop)  # equivalent legacy function call
True

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. 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.
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 COLA within tol, False otherwise

See also

closest_STFT_dual_window: Allows determining the closest window meeting the COLA constraint for a given window
check_NOLA: Check whether the Nonzero Overlap Add (NOLA) constraint is met
ShortTimeFFT: Provide short-time Fourier transform and its inverse
stft: Short-time Fourier transform (legacy)
istft: Inverse Short-time Fourier transform (legacy)

Notes

In order to invert a short-time Fourier transfrom (STFT) with the so-called “overlap-add method”, the signal windowing must obey the constraint of “Constant OverLap Add” (COLA). This ensures that every point in the input data is equally weighted, thereby avoiding aliasing and allowing full reconstruction. Note that the algorithms implemented in ShortTimeFFT.istft and in istft (legacy) only require that the weaker “nonzero overlap-add” condition (as in check_NOLA) is met.

Some examples of windows that satisfy COLA:

Rectangular window at overlap of 0, 1/2, 2/3, 3/4, …
Bartlett window at overlap of 1/2, 3/4, 5/6, …
Hann window at 1/2, 2/3, 3/4, …
Any Blackman family window at 2/3 overlap
Any window with noverlap = nperseg-1

A very comprehensive list of other windows may be found in [2], wherein the COLA condition is satisfied when the “Amplitude Flatness” is unity.

Added in version 0.19.0.

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

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

COLA is not true for 25% (1/4) overlap, though:

>>> signal.check_COLA(signal.windows.boxcar(100), 100, 25)
False

“Symmetrical” Hann window (for filter design) is not COLA:

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

“Periodic” or “DFT-even” Hann window (for FFT analysis) is COLA for overlap of 1/2, 2/3, 3/4, etc.:

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

>>> signal.check_COLA(signal.windows.hann(120, sym=False), 120, 80)
True

>>> signal.check_COLA(signal.windows.hann(120, sym=False), 120, 90)
True