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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?

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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.

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  • $\begingroup$ Interesting, I don't have access to Matlab, but is it possible to do it in octave? $\endgroup$ Mar 24 '16 at 1:16
  • $\begingroup$ I have not used it, but there does seem to be a signaling package: octave.sourceforge.net/signal $\endgroup$
    – dmb
    Mar 24 '16 at 1:18
  • $\begingroup$ Thanks! As I've achieved a mini-victory spotting this sine wave after modifying the input data, I'll reward myself and go to bed now! I'll experiment with Octave in the morning! $\endgroup$ Mar 24 '16 at 1:23
  • $\begingroup$ Am I right in assuming that peaks in the positve mean the signal has that particular frequency and negative troughs mean the frequency is present, but out of phase? How exactly do I determine the precise phases of the sines? $\endgroup$ Mar 24 '16 at 20:26

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