Skip to main content
`Ctrl`+`K`
scipy.signal.

# check_COLA

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

  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:
    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 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