I have given the periods found in the absolute (I use this term in the mathematical sense meaning unsigned) barycentre motion over 512 years from 1500 to 2011. For comparison we should have the best determination of periods in the sunspot cycles over the same period, but reliable data only begins at about 1700, so will have to make do with the period 1700 to 2006. Because FFT only determines cycles that fit exactly into the interval this means that cycles periods would be rather coarse with this amount of data. For example, the difference between 27 and 28 cycles in 306 years is a period of 11.33 or 10.93 years. So methods that interpolate between the FFT values are needed.

One published paper that satisfies this requirement is by Olvera (pdf)(1). It has a graph that shows the spectrum of the sunspot cycle over a wide range of periods with the amplitude shown on a log scale. It is based on a periodogram method. It does not lable of list all the peaks in the spectrum, so I have enlarged the part of interest and read the values off and labeled a copy of that graph.

Just to be sure, I have used another method of measuring between the whole number of periods that FFT allows which compares sine waves with different periods to the sunspot record and finds the maximum covariance for each period (the maximum occurs when the phase is the same on average). I produced a graph of this for the range ~8 to ~14 years where the main action is taking place.

Just a cycles purist note: It should be understood that both Olvera's method and mine are measuring the frequency (or period) at closer intervals than FFT and so will get a finer result. But they still do not allow for the effect of interference between close frequencies and the ideal method is MESA (maximum entropy spectral analysis) which I don't have a working program for. So there may be displacements of peaks slightly when other major peaks are close to them in terms of how many cycles fit in the entire period - if within 1 or 2 or even 3 cycles they will have some effect.

{Hi Jim, I cannot work out how to put in a thumb to a graphic, so I am putting in just one and links to the other two. Can someone please tell me how to do thumb nail ghraphics?}

This is my analysis of the sunspot periods in the range ~8 to ~14 years. The numbers given are based on determinations at closer intervals (.01) than those ploted here (.1).


The spectrum by Olvera I have loaded here and the magnified and labeled part is here.

In a separate post I will tabulate the various cycles periods found in sunspots and in the barycentre motion for comparison now that we have good publicly available data on all of these.

References:

(1) ECE 538: STATISTICAL SIGNAL PROCESSING I, A Spectral Analysis of the Sunspot Time Series Using the Periodogram, Felipe E. Olvera, Jr., Student Member, IEEE