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Wondering about the resconstruction of the input signal when an overlapped windowing function has been applied.

I'm specifically applying a Hamming window with 50% overlap and I wish to reconstruct the input signal.

Here http://www.dsprelated.com/showthread/comp.dsp/105321-1.php it's given that summing the 50% overlapped windows gives a sum of 1.08.

In order to reconstruct the input signal (with the same exact amplitudes), then can I merely subtract the extra ~".08" from all the samples? Or, equivalently, divide by 1.08?

The overlapp-add does not result into the exact same signal though, but there's some miniscule variation for some reason. By testing with an array of 1.0s I get back varying values that are of the form 0.999 ...

I guess reconstructing doesn't always lead to the same exact input signal, depending on the windowing function and the amount of overlap?

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  • $\begingroup$ What is the percentage difference from 1.0? Any FFT processing will introduce a tiny amount of rounding error or numerical noise, likely well below the S/N of any physical data. $\endgroup$ – hotpaw2 Jul 1 '15 at 17:25
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did you ask this at comp.dsp? appears so. if you do what hotpaw says, your Hamming window will be

$$ w(t) = \begin{cases} 0.426 \cdot \cos(\pi t) + 0.5 & \text{if }|t| < 1 \\ 0.037 & \text{if }|t| = 1 \\ 0 & \text{if }|t| > 1 \end{cases} $$

still a Hamming window, but it overlap-adds to 1 (with 50% overlap), rather than 1.08.

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If your process has a gain of 1.08, then you will need to divide the processes result by 1.08, not subtract a constant.

Finite numerical processes involving transcendental functions should not be expected to produce exact results in the general case. Common fast computer processor arithmetic is "only" accurate to about a dozen significant digits.

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