Determining if a dataset approximates a sine wave

Question

Is there an algorithm that can be used to determine whether a sample of data taken at fixed time intervals approximates a sine wave?

Answer 1

Take the fourier transform which transforms the data into a frequency table (search for fft, fast fourier transformation, for an implementation. For example, FFTW). If it is a sinus or cosinus, the frequency table will contain one very high value corresponding to the frequency you're searching for and some noise at other frequencies.

Alternatively, match several sinussen at several frequencies and try to match them using cross correlation: the sum of squares of the differences between your signal and the sinus you're trying to fit. You would need to do this for sinussen at a range of frequencies of course. And you would need to do this while translating the sinus along the x-axis to find the phase.

Answer 2

You can calculate the fourier transform and look for a single spike. That would tell you that the dataset approximates a sine curve at that frequency.

Answer 3

Shot into the blue: You could take advantage of the fact that the integral of a*sin(t) is a*cos(t). Keeping track of min/max of your data should allow you to know a.

Answer 4

Check the least squares method.

@CookieOfFortune: I agree, but the Fourier series fit is optimal in the least squares sense (as is said on the Wikipedia article).

If you want to play around first with own input data, check the Discrete Fourier Transformation (DFT) on Wolfram Alpha. As noted before, if you want a fast implementation you should check out one of several FFT-libraries.