def periodic_hann(window_length):
"""Calculate a "periodic" Hann window.
The classic Hann window is defined as a raised cosine that starts and
ends on zero, and where every value appears twice, except the middle
point for an odd-length window. Matlab calls this a "symmetric" window
and np.hanning() returns it. However, for Fourier analysis, this
actually represents just over one cycle of a period N-1 cosine, and
thus is not compactly expressed on a length-N Fourier basis. Instead,
it's better to use a raised cosine that ends just before the final
zero value - i.e. a complete cycle of a period-N cosine. Matlab
calls this a "periodic" window. This routine calculates it.
Args:
window_length: The number of points in the returned window.
Returns:
A 1D np.array containing the periodic hann window.
"""
return 0.5 - (0.5 * np.cos(2 * np.pi / window_length *
np.arange(window_length)))
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