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Reconstruction of window function using the raw signal & smoothed signal

Posted 1 month ago
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Hey everyone,

I am stuck in the following scenario. I have a smoothed signal and the raw signal was derived from. Also, I know the length of the applied window but not its structure.

What I want is the window function in the time-domain and I want to analyze the function in the frequency domain (for spectral leakage).

My thought process was the following:

  • y(t) = (x*h)(t) : The smoothed signal is a convolution of the raw signal and the window function
  • Y(s) = X(s)H(s): Applying DFT
  • DFT^-1(Y(s)/X(s)) = h(t): Rearranging and Inverse-DFT

However, I don't know how to incorporate the length of h(t). Thus, calculation in Mathematica yields a window function with the same length as the other two signals.

Is it even possible to recreate the signal the way I intend to?

Cheers, Oliver

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