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I am a newbie in signal processing. I am testing the Hanning window on a signal. Obviously doing this window also means cut some energy of the signal, and when I do the DFT, the 0 frequency is not equivalent anymore to the average of the time history. Do you usually solve in some way this problem? Can someone suggest papers or books where noise-reducing strategies for the FT of a signal are investigated? I just don't know how to start, an online search didn't give me more than basic definition (so please don't send me the Wikipedia definition of the tapering window)

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  • $\begingroup$ Hm, I find difficult to relate Hanning window, the DC frequency, and noise reduction in the frequency domain. What kind of signals are you dealing with? $\endgroup$
    – GKH
    Jan 19, 2020 at 15:03
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    $\begingroup$ In a nutshell, you must normalize the energy by the energy of the window. In case of simple magnitude, this means dividing by the sum of window samples. This publication has great explainations. $\endgroup$
    – jojeck ♦
    Jan 19, 2020 at 15:03
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    $\begingroup$ Excellent reference, thank you for reminding me it is in my "to read in a serious manner" list for a while $\endgroup$
    – Laurent Duval
    Jan 19, 2020 at 15:15

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I suspect you are talking about the Hann window, after Julius von Hann, and Blackman & Tukey. Of course, a non-constant window may induce energy variations, either used as a weighted average, or a convolutional filter. This can be compensated in several ways:

  • by normalizing the window amplitudes
  • by separating tipme-portions, or signal components, like removing the mean or low-frequencies before doing the processing
  • by modelling the signal and applying model-based corrections.

More would be needed on your signal to provide more precise answers. R. Lyons on a diagram on page xviii of his book Understanding Digital Signal Processing highlights the importance of windows.

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