Well - ok! I do admit that I was simply not willig to even consider a bug in a function which belongs to the prominent Fourier-family ...

At least PeriodogramArray[] seems to give a correct result:

n = 100;
data = Cos[2 \[Pi] Range[0, n - 1]*0.25] // N;
pdg = Periodogram[data, PlotRange -> All, ScalingFunctions -> {"Linear", "Linear"}, PlotStyle -> Dotted];
pdata = MapIndexed[{(First[#2] - 1)/n, #1} &, PeriodogramArray[data]];
Show[ListLinePlot[pdata[[;; 50]], PlotRange -> All, GridLines -> {{.25}, None}], pdg]

Hi Vladimir, yes that is a bug. It is due to an incorrect setting of the DataRange option. To correct please see the attached notebook.

Attachments:

For Vladimir- Pe...nb

Henrik, the discrete Fourier transform works for any signal, not only for ones with the first and last elements equal.

We can check it formally, making sure that the explicit inverse Fourier transform

Table[Chop[1/Sqrt[n] (Fourier[data] . Table[Exp[-2 \[Pi] I t s / n ], {s, 0, n-1}])], {t, 0, n-1}]

brings us back to the initial data. And this expression, in the case of my signal, includes Exp[-2 [Pi] I t * 0.25 ] rather than Exp[-2 [Pi] I t * 0.255102 ], so the true frequency must be 0.25.

Why? Length[Range[0,100-1]] is 100.