I have a signal composed of 3 waves oscillating at a high frequency (~10^15 Hz) separated in frequency by 10MHz. I want to simulate the resulting beat wave spectrum. I am expecting a two-peak spectrum, one at 10Mhz and the other one at 20Mhz, due to the beating. Using this code:
\[Omega] = 437653.22*10^9;
A = 1;
\[CapitalOmega] = 10*10^6;
\[Beta] = 0.1;
E0[t_] :=
A*(Exp[I*\[Omega]*t] + \[Beta]*
Exp[I*(\[CapitalOmega] + \[Omega])*t]/2 - \[Beta]*
Exp[I*(\[CapitalOmega] - \[Omega])*t]/2);
data = Table[{t, E0[t]}, {t, 0, 1*10^-6, 1*10^-9}];
ListLinePlot[
Re[data[[All, 2]]],
AspectRatio -> 1/4,
Mesh -> All,
MeshStyle -> Directive[PointSize[Small], Red],
Frame -> True
]
Periodogram[
data[[All, 2]],
SampleRate -> 50*10^6,
Frame -> True,
GridLinesStyle -> Directive[Red, Dashed],
AspectRatio -> 1/4,
PlotRange -> All
]
I managed to get a two-peak spectrum, but the peaks are in the wrong positions. How can I fix that?