Although I am using software and code for this problem , I figured my issue is more mathematical. I am trying to fit a sine wave to some (noisy) data. When you look at the data it does resemble a sine and in theory it should have a fixed Frequency. However due to noise the frequency is not constant at all (it has small random shifts). Therefore I want to find a sine equation whose frequency varies.
I was thinking of an equation of the sort:$$Asin(ax^n + bx^{n-1}+ ... +z)$$ where the frequency is a polynomial function of degree $n$. However This does not seem to work. My question is simple since I only want to know If i'm on the right track. Does a polynomial frequency make sense for a sine which has varying (random) frequency?