Based on the above referenced (and unreferenced) answers on mathematica.stackexchange, here is a short version of running code:
data=Au4; (* input *)
timeInterval = 10; (* input *)
nSamples = Length@data;
dt=timeInterval/nSamples;
spectrumLength = Floor[0.5 nSamples];
powerSpectralDensity = Abs[Fourier[signal][[;; spectrumLength]]]^2;
freqs = Range[0, spectrumLength - 1]/(dt*nSamples);
plot = ListLogLogPlot[Transpose[{freqs,powerSpectralDensity}]]
Seeing is believing, so here is the code applied to a simple sine wave:
- Frequency is 0.5.
- Duration of sampled time interval is 20.
- Number of discrete samples in interval is 1000.
Code:
nSamples=1000;
timeInterval=20.0;
dt=timeInterval/nSamples;
f=0.5;
signal=Table[Sin[2.0 Pi f t dt],{t,nSamples}];
ListLinePlot[signal,Frame->True,DataRange->{0,timeInterval},FrameLabel->{"time","signal"},Mesh->All,MeshStyle->Directive[AbsolutePointSize[4],Black],PlotRangePadding->{None,Automatic},FrameStyle->Directive[Black,20,FontFamily->"Helvetica",AbsoluteThickness[2]]]

spectrumLength=Round[0.5 nSamples];
powerSpectralDensity=Abs[Fourier[signal][[;;spectrumLength]]]^2;
freqs=Range[0,0.5/dt,0.5/(dt(spectrumLength-1))];
ListLogLogPlot[Transpose[{freqs,powerSpectralDensity}],Frame->True,Joined->True,PlotRange->All,PlotRangePadding->None,GridLines->{{f},None},GridLinesStyle->Directive[Red,Dashed],FrameLabel->{"frequency f","power spectral density"},PlotRangePadding->{None,Automatic},FrameStyle->Directive[Black,20,FontFamily->"Helvetica",AbsoluteThickness[2]]]

Periodogram
with optionSampleRate
$\endgroup$