How to Ascertain Sine Wave and Harmonics I have some data that I've noticed conforms to a sine wave. Details of the data is unknown. My task is to approximate it as closely as possible.

From some experimentation in Excel, I noticed the data follows a sine wave, so attempted to plot in the base sine wave (orange) and am now trying to approximate the blue line. I believe this is a simple job of harmonics being added to the base sine wave, however; the quantity and their respective amplitude and harmonic number (2nd harmonic being 2 * f, 3rd harmonic being 3 * f etc) is what I now need to calculate. I'm also guessing the amplitude of the resulting wave is modified by possibly a sine wave too.

Is there software which could automate this and approximate it through some analysis (Fourier analysis maybe) or possibly brute force, or is it something I have to write myself?
You want to look at the spectral density to get an idea of the distribution of the frequency components. Check out the 'psd' package in r or the signal processing toolbox if you have access to Matlab.