When calculating the marginal Hilbert spectrum of a discretely sampled harmonic oscillation (sine wave), I have found that the peak in the spectrum has a roughly Lorentzian line shape, albeit approximate and with crude sampling. I was wondering what the origin this line shape is for the marginal Hilbert Spectrum?

Analysis of the instantaneous frequency as a function of time indicates that the individual time components of the oscillation mostly contribute to the central frequency (no surprise there), but also that the moments giving rise to the higher and lower frequency components are seemingly random, by eye at least.



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