check_COLA(window, nperseg, noverlap, tol=1e-10)
In order to enable inversion of an STFT via the inverse STFT in istft
, it is sufficient that the signal windowing obeys 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.
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 , wherein the COLA condition is satisfied when the "Amplitude Flatness" is unity.
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.
Length of each segment.
Number of points to overlap between segments.
The allowed variance of a bin's weighted sum from the median bin sum.
:None:None:`True` if chosen combination satisfies COLA within :None:None:`tol`, :None:None:`False` otherwise
Check whether the Constant OverLap Add (COLA) constraint is met.
check_NOLA
Check whether the Nonzero Overlap Add (NOLA) constraint is met
istft
Inverse Short Time Fourier Transform
stft
Short Time Fourier Transform
>>> 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) TrueSee :
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.lombscargle
scipy.signal._spectral_py.istft
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