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I have time series of 3 signals, and I found the amplitude of vibration waveform would display the so-called beat phenomenon, which means the amplitude at different time is not always equal, and the beat envelope is also different.

The time history of these signals looks like enter image description here

It seems that the signal-1 has quick and strong periodic beat, signal-2 has slow and periodic beat, while signal-3 has slow but random beat. So I am wondering is there any indicator to quantify this beat phenomenon of amplitude, like "kurtosis" and "skewness" to measure the peak shape and symmetry of waveform.

And another question is some waveform is not perfectly sinusoid, and again, is there any method to measure the deformation degree of waveform?

Thanks!

WUYing
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    Have you considered expressing these signals in the frequency domain? – Drew Oct 04 '22 at 04:51
  • Adding to the comment by @Drew, computing the Fast Fourier Transform of your signal will provide you more information. Amongst others, I personally find Matlabs examples to be quite informative: https://se.mathworks.com/help/matlab/ref/fft.html – ToxicOwl Oct 04 '22 at 11:59
  • @Drew Thanks! Yes, I have do the FFT and PSD of these signals, and the frequency and energy content can give me some information, but there is still no good quantitative indicators to measure the beat phenomenon in the time series of signal, like some beats are smooth wave with different wave length (1 and 2), some are pitchforks (3). – WUYing Oct 04 '22 at 17:43

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