Off[Fourier::fpopt2];

FindPeriod[x_List, SampleRate_] := 
Module[{m = Length[x], aft, b, y, \[Delta], afrft, k, mean},
	mean = Tr[x]/m;
	aft = Drop[Abs[Fourier[x - mean]],-1];
	b = Position[aft, Max[aft]][[1, 1]];
	If[aft[[b + 1]] < aft[[b - 1]], b--];
	b--;
	y = x Exp[2 \[Pi] I b Range[0., m - 1]/m];
	\[Delta] = 1./m;
	afrft = Abs[Fourier[y, FourierParameters -> {0, \[Delta]}]];
	k = Position[afrft, Max[afrft]][[1, 1]] - 1;
	SampleRate m/(b + k \[Delta])]