A frequency domain transformation of the data

Using autocorrelation

$$\begin{gathered} \mathrm{with}\left(\mathrm{SignalProcessing}\right)\: \\ \mathrm{with}\left(\mathrm{plots}\right)\: \\ \mathrm{with}\left(\mathrm{DataSets}\right)\: \end{gathered}$$

$\mathrm{DataReference}≔\mathrm{Reference}\left(''quandl''\,''SIDC/SUNSPOTS\_A''\right)$

$\mathrm{DataReference}≔\left[\begin{array}{c}\mathrm{Data\; set}\\ \mathrm{Sunspot\; Numbers\; (Annual)}\\ \mathrm{Quandl\; SIDC/SUNSPOTS\_A}\\ \mathrm{up\; to\; 314\; rows\; (annual),\; 1\; column}\\ \mathrm{1700-12-31\; -\; 2013-12-31}\end{array}\right]$

$\mathrm{data}≔\mathrm{convert}\left(\mathrm{DataReference}\, \mathrm{Matrix}\right)\:$

$\mathrm{DocumentTools}:-\mathrm{Tabulate}\left(\left[''Notes''\,\mathrm{GetDescription}\left(\mathrm{DataReference}\right)\right]\,\mathrm{weights}\=\left[20\,80\right]\right)$

$\mathrm{SunspotNumber}≔\mathrm{data}\left[..\,2\right]\:$

$\mathrm{ParseYear}≔x\to \mathrm{StringTools}:-\mathrm{ParseTime}\left(''\%Y-\%m-\%d''\,x\right):-\mathrm{year}\:$

$\mathrm{Year}≔\mathrm{ParseYear}~\left(\mathrm{data}\left[..\,1\right]\right)\:$

$\mathrm{pointplot}\left(\left[\mathrm{seq}\left(\left[{\mathrm{Year}}_i\,{\mathrm{SunspotNumber}}_i\right]\,i\=1..314\right)\right]\,\mathrm{labels}\=\left[''Year''\,''Wolf\; Number''\right]\,\mathrm{labeldirections}\=\left[\mathrm{horizontal}\,\mathrm{vertical}\right]\,\mathrm{connect}\=\mathrm{true}\,\mathrm{title}\=''Sunspot\; Data''\, \mathrm{titlefont}\=\left[\mathrm{Arial}\,14\right]\,\mathrm{thickness}\=0\, \mathrm{gridlines}\, \mathrm{size}\=\left[800\,''golden''\right]\right)$

$\mathrm{fSunspots}:=\mathrm{FFT}\left(\mathrm{SunspotNumber}\left[1..2^8\right]\right)\:$

$\mathrm{samplingRate}:=1\:$

$\mathrm{psSunspots}:=\mathrm{PowerSpectrum}\left(\mathrm{fSunspots}\right)\:$

$\mathrm{SignalPlot}\left(\mathrm{psSunspots}\left[2..\frac{\mathrm{numelems}\left(\mathrm{psSunspots}\right)}{2}\right]\, \mathrm{samplerate}\=2^8\,\mathrm{labels}\=\left[''Frequency\; (1/years)''\,''Power''\right]\,\mathrm{title}\=''Power\; Spectrum''\,\mathrm{titlefont}\=\left[\mathrm{Arial}\,14\right]\, \mathrm{size}\=\left[800\,''golden''\right]\right)$

$\mathrm{period}:=\frac{1}{0.09}$

$\mathrm{period}≔11.11111111$

$\mathrm{aSunspotNumber}:=\mathrm{AutoCorrelation}\left(\mathrm{SunspotNumber}\right)\:$

$\mathrm{SignalPlot}\left(\mathrm{aSunspotNumber}\left[1..36\right]\,\mathrm{labels}\=\left[''Years''\,''''\right]\,\mathrm{title}\=''Autocorrelation\; of\; Sunspot\; Data''\,\mathrm{titlefont}\=\left[\mathrm{Arial}\,14\right]\,\mathrm{size}\=\left[800\,''golden''\right]\right)\;$