i'm currently working on feature extraction from noisy (real world measurement) sinusoid measurements. I was thinking about fitting a propability distribution over my signals propability to use the fitting parameters as signal features for further use in clustering etc.

Unfortunately, i was not able to find a suitable propability distribution function structure. The propability distribution of a noisy sinusoid should look like a smooth "M".

i found this:

https://stats.stackexchange.com/questions/199215/probability-distribution-of-a-sine-wave

but to my understanding, this cannot be applied to a noisy sinus.

Best Regards and many thanks in advance