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This question is an extension to the question about WVD vs STFT originally posted Here. During the QA it was pointed out that the WVD only works for noiseless signals.

To test that out I created a simple chirp signal in MATLAB and compared WVD spectrograms at different SNRs.

Below is the time-domain signal on the left and the WVD corresponding WVD on the right for 25dB SNR:

Time-Domain Chirp Signal and WVD at 25dB SNR

Below is for the 0dB SNR case:

Time-Domain Chirp Signal and WVD at 0dB SNR

Even at 0dB SNR the presence of chirp is still visible in the WVD spectrogram, is MATLAB doing any other post-processing as well? and is the WVD really useless for time-frequency analysis of real-world signals?

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  • $\begingroup$ I suggest checking if there's windowing by default in the implementation, and asking separately about WVD's interferences, which'll shed light on this question as STFT doesn't have this problem. $\endgroup$
    – OverLordGoldDragon
    Commented Jan 21, 2023 at 10:41
  • $\begingroup$ Ok, ill check that out, kindly elaborate WVD's interferences? $\endgroup$
    – malik12
    Commented Jan 21, 2023 at 14:56
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    $\begingroup$ you can detect signals below noise level, provided they have strong enough autocorrelation, so even when noise stronger that weak signal, noise does no autocorrelate, yet a correctly designed chirp may be detectable. OFDM-based systems also exhibit this strength. $\endgroup$
    – John Bofarull Guix
    Commented Jan 28, 2023 at 17:39

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