How do we apply windowing of 50% (4 samples) to a discrete signal with the odd number of values as 1234567?
Is it done as: 1234 3456 567(0)
or 1234 3456 67(0)(0)?
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Depending on the window function, you may be able to use a DFT-even version of the window function. "DFT-even" means that the periodic extension of the window function is symmetrical. In MATLAB and Octave you can get such a window like this (the first line in the source code):
a = hanning(10, "periodic");
b = fftshift(a);
c = a + b;
plot(a, "x", b, "o", c, "+");
Figure 1. DFT-even Hann window (blue x), shifted DFT-even Hann window (red o) and their sum (orange +).
The window function and the shifted window function have in some sense a 50 % overlap, and they sum to a constant, which I think was the desired quality that the 50 % overlap was though to facilitate.
Not a problem in the above, but if the window function is such that it does not end at a zero value, and the start and the end values are not equal, then one possibility would be to move one half of the value of the last sample to just before the first sample.
answered Sep 28 '20 at 10:23
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1$\begingroup$ Nice Olli. And we should note that most higher performance windows require much more overlap to achieve this unity (75% typical). $\endgroup$ – Dan Boschen Sep 28 '20 at 18:16
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1$\begingroup$ @DanBoschen yep it depends on the window function. For window functions made of cosine terms, see this answer for the overlap that gives a constant sum. $\endgroup$ – Olli Niemitalo Sep 28 '20 at 18:57
12345678? And then consider if the value for sample 8 was 0 $\endgroup$ – Dan Boschen Sep 28 '20 at 4:00