NOTE: www-users.cs.york.ac.uk/~fisher/mkfilter
seems to be down so I used Mathematica to generate the below 4th order Butterworth with .2 corner frequency:
tf = ButterworthFilterModel[{4,2 Pi/5}]
dtf=ToDiscreteTimeModel[tf,1,z] 
which I've incorporated into the below code.

Note: If you downloaded SunSpot2.m, you must place it where Mathematica can find it


x=<<SunSpot2.m

y=Table[0,{i, 2052}];
Do[
y[[n]]=x[[n-4]]+4 x[[n-3]]+6 x[[n-2]]+4 x[[n-1]]+x[[n]]+
 (1.11894 ) y[[n-1]] - (0.884346) y[[n-2]] + (0.289792 ) y[[n-3]]- (0.0445722) y[[n-4]],{n,5,2052}]

ListPlot[y, Joined->True, PlotRange->All]
ListPlot[x, Joined->True, PlotRange->All]

data=Drop[y,4]

Data=Fourier[data]
Data=RotateLeft[Data,1]
ListLinePlot[Abs[Data],PlotRange->All]
ListLinePlot[Abs[Data],PlotRange->{{1,50},All}]

ListLinePlot[Abs[Data[[1;;20]]],PlotRange->All]  


---
For comparison, if you don't Low Pass (i.e., use the raw x)
there is noise throughout the Fourier Data.  Of course near
the peak (which is at low frequency) there isn't much difference 
(aside from the amplification) between y-Fourier and x-Fourier

data=Drop[x,4]
Data=Fourier[data]
Data=RotateLeft[Data,1]
ListLinePlot[Abs[Data],PlotRange->All]