finding period of periodic signal with varying amplitude I have some data from experiment as shown in the figure. It looks roughly sinusoidal, but with an increasing amplitude, probably due to attenuation of the signal at different measured position. What is the best way to find the period? I am thinking of something like fourier transform or auto-correlation, but I'm not sure if they are applicable to signal with varying amplitude, and for non-uniformly sampled data.

 A: Fourier transforms are applicable to any signal, even aperiodic ones. When analyzing your data, a Fourier transform will show extra frequencies due to the changing amplitude, but the frequency with the largest amplitude will still be the obvious one.
However, the fact that your data points are not equally spaced in the x-axis is a problem. Numerical Fourier and autocorrelation functions assume data is equally spaced in the independent variable. You'll probably want to investigate non-linear fitting and regression. Basically, you start with a function with several parameters and successively improve the approximation. In your case,
$$y(x) = \alpha\sin(\beta x + \gamma) + \epsilon$$
or
$$y(x) = (\alpha + \delta x)\sin(\beta x + \gamma) + \epsilon$$
if you want to be fancy. The goal is to find values for the Greek letters. A computer program would start with rough guesses and slowly change them until the errors between the fitted curve and the data stopped decreasing. Your period will then be $2\pi/\beta$.
If you only care about the period, a more direct method for estimating is to find the average horizontal distance between successive peaks and troughs and double that value.
