numpy.hanning#

numpy.hanning(M)#

Return the Hanning window.

The Hanning window is a taper formed by using a weighted cosine.

Parameters:: M (int) – Number of points in the output window. If zero or less, an empty array is returned.
Returns:: out – The window, with the maximum value normalized to one (the value one appears only if M is odd).
Return type:: ndarray, shape(M,)

Notes

The Hanning window is defined as

$w(n) = 0.5 - 0.5\cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1$

The Hanning was named for Julius von Hann, an Austrian meteorologist. It is also known as the Cosine Bell. Some authors prefer that it be called a Hann window, to help avoid confusion with the very similar Hamming window.

Most references to the Hanning window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means “removing the foot”, i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function.

References

Examples

>>> import numpy as np
>>> np.hanning(12)
array([0.        , 0.07937323, 0.29229249, 0.57115742, 0.82743037,
       0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249,
       0.07937323, 0.        ])

Plot the window and its frequency response.

numpy.hanning#

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