If I wanted to plot a spectrogram of a signal, I would by default use the Short Time Fourier Transform. However, the Hilbert transform does something similar: it lets us calculate instantaneous frequencies. So one could plot the Hilbert Spectrum using this transform instead.

What are the differences (if any) between these two approaches? In which cases would one be better than the other?

  • $\begingroup$ HT will not really produce a spectrogram. What you get instead is a 1D plot of the instantaneous frequency. In theory, you could overlay that trace on top of the original spectrogram. $\endgroup$ – jojek Dec 14 '17 at 14:02
  • $\begingroup$ @jojek I might have understood things wrong. I'm just starting to read about Hilbert transform - never used it before. But as I see it, one can use the Hilbert spectrum to make a 3D plot, right? I mean, it appears to be a two-variable function... $\endgroup$ – Tendero Dec 14 '17 at 14:07
  • $\begingroup$ So you want to obtain the Hilbert Spectrum then. $\endgroup$ – jojek Dec 14 '17 at 14:11
  • $\begingroup$ @jojek Thanks for the edit and clarification, I mixed the two concepts up. $\endgroup$ – Tendero Dec 14 '17 at 14:15

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