Talk:S transform

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How do we estimate instantanious frequency of a signal using S-transform ?

You don't. Instantaneous frequency shows you the dominant frequency at each time sample of the signal. Time-frequency representations like the S-transform show you all the magnitudes (and phases) of each frequency component at each time sample. So the instantaneous frequency would be something like finding the frequency with the highest magnitude at each time sample. However, this assumes that there is only one peak frequency and sometimes this is not the case. In this case the instantaneous frequency calculation will be all messed up. This is why time-frequency representations are used. Hamsterlopithecus (talk) 19:22, 21 January 2016 (UTC)

Actually, you can and do; and it can be done for any time-frequency transform (e.g. Windowed Fourier, Gabor, Spectrogram) and time-scale transform (e.g. Wavelet, S-Transform), in essentially the same way. Both instantaneous frequency (and time) estimation and relocation are included in the Time-Frequency Toolbox, for instance. You will also find discussion of instantaneous time and frequency (and methods for estimating them) on the Wikipedia under this topic. The main assumption is that the raw transform serves its end of separating the underlying components of the actual signal well enough that each frequency or "voice" of the transform contains a contribution from only one component, rather than from two or more. When this occurs, (1) the usual formula (instantaneous frequency = time rate of change of phase) can be applied to each channel and (2) any two channels that carry the same component will produce the same results, so that the usual consolidation of the spectrum occurs when the spectrum is frequency-relocated. The differentials of the phase can be estimated (up to winding number ambiguity) by taking discretized derivatives or algebraically (since the transform of a partial differential operator is a product operator). Both methods are used. To give you an example, available here https://www.youtube.com/watch?v=6ZpVBUVab7Q (at the time of writing), I put up a small segment of Acid Trax with a scalograph both raw and frequency-relocated ... coded with amplitude as brightness and phase as color (27.5-3520 Hz, equal spacing between octaves, 1 horizontal pixel = 1/1320 second). — Preceding unsigned comment added by 2605:A000:1401:8806:222:69FF:FE4C:408B (talk) 00:33, 17 August 2019 (UTC)