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# scipy.signal.check_NOLA

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

  Check whether the Nonzero Overlap Add (NOLA) constraint is met.

  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 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