Wednesday, 2 December 2015

frequency - How to find period/envelope that is larger than sample size?


Mercury's distance from the solar system's barycenter (in kilometers) can be approximated as:


5.9115960588705115e7 + 1.1573608483842954e7*Cos(2.086944367456105 - 0.0029751428085695573*t) 

based on 8 years worth of hourly "samples" from HORIZONS. (t is in hours; I forget what value corresponds to t=0, but it should be irrelevant to my question).


The residuals after this approximation look like this:


enter image description here



I could add additional Fourier coefficients, but there appears to be a period or envelope that is larger than the sample size.


Standard Fourier analysis will never find this period, and continuous Fourier analysis is fairly inefficient.


How can I find this period/envelope?


Perhaps more to the point: what's the simplest function that does a "fairly good" job of approximating this data?


The graph shows a pattern, so there "must be" such a function?




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