Difference in output of even-length window function

Introduction

There are multiple ways to generate a window function, which is widely used in signal processing, with python. Since the behavior is slightly different depending on the generation method, record it as a memorandum. (Limited to humming windows here. Maybe similar things happen with any window)

Comparison

There are three types of candidates to compare. The window width is $ N $.

• numpy.hamming(N)
• scipy.signal.hamming(N)
• scipy.signal.get_window('hamming', N)

Comparison result

Same when $ N $ is odd.

>>> import scipy.signal, numpy
>>> N = 5
>>> numpy.hamming(N)
array([ 0.08,  0.54,  1.  ,  0.54,  0.08])
>>> scipy.signal.hamming(N)
array([ 0.08,  0.54,  1.  ,  0.54,  0.08])
>>> scipy.signal.get_window('hamming', N)
array([ 0.08,  0.54,  1.  ,  0.54,  0.08])

However, the situation changes when $ N $ becomes an even number. (get_window)

>>> import numpy, scipy.signal
>>> N = 4
>>> numpy.hamming(N)
array([ 0.08,  0.77,  0.77,  0.08])
>>> scipy.signal.hamming(N)
array([ 0.08,  0.77,  0.77,  0.08])
>>> scipy.signal.get_window('hamming', N)
array([ 0.08,  0.54,  1.  ,  0.54])

However, if you put False in the third argument of get_window, the result will be the same.

>>> scipy.signal.get_window('hamming', N, False)
array([ 0.08,  0.77,  0.77,  0.08])

why

scipy.signal.hamming and numpy.hamming are by default Generate the value of the window function so that it is symmetrical. On the other hand, get_window generates a" periodic "(?) Value for ease of use in the FFT. Setting the third argument to False produces a symmetric value that is easy for the filter to use.

Therefore, the default behavior differs depending on the function.

References

http://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.hamming.html http://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.get_window.html