Window function constant overlap-add conditions (COLA)

readme.md

Fractions of overlap that result in COLA condition for all SciPy windows:

• barthann: 1/2, 3/4, 5/6, 7/8, 9/10, 11/12, 13/14, ...
• bartlett: 1/2, 3/4, 5/6, 7/8, 9/10, 11/12, 13/14, ...
• blackman: 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, ...
• blackmanharris: 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, ...
• bohman:
• boxcar: 0, 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, ...
• chebwin:
• cosine:
• exponential:
• flattop: 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, ...
• gaussian:
• general_gaussian:
• hamming: 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, ...
• hann: 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, ...
• kaiser:
• nuttall: 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, ...
• parzen: 3/4, 7/8, 11/12, 15/16, 19/20, 23/24, ...
• slepian:
• triang: 1/2, 3/4, 5/6, 7/8, 9/10, 11/12, ...
• tukey: 3/4, 5/6, 7/8, 9/10, 11/12, 13/14, ...

See also "AF" graphs in https://holometer.fnal.gov/GH_FFT.pdf

overlaps.py

from __future__ import division, print_function, absolute_import
import numpy as np
import scipy
from spectral import check_COLA  # https://github.com/scipy/scipy/pull/6058

windows = np.unique(scipy.signal.windows._win_equiv.values())
windows = sorted(windows, key=lambda x: x.__name__)

for window in windows:
    try:
        print(window.__name__, end=': ')
        for num in range(10):
            if check_COLA(window(1000*(num+1), sym=False),
                          1000*(num+1), 1000*num):
                print('{}/{}'.format(num, num+1), end=', ')
        print()
    except:
        print()
        continue