You can, but it’s not trivial. It’s described mathematically Angle sum and difference identities and Product-to-sum and sum-to-product identities. You have to heterodyne it by mutltiplying it by the appropriate carrier frequency (creating a double-sideband, suppressed-carrier signal), then filter the unwanted sub-harmonic (at 50 Hz here), with a bandpass filter. My filter design procedure is here: How to design a lowpass filter for ocean wave data in Matlab? Note that this will work for frequency-shifting pure frequencies as well as modulated frequencies. (It’s the principle behind amplitude modulated wireless transmission and reception, where a baseband signal is heterodyned to frequency suitable for transmission, and at the other end, to do essentially the opposite in a superheterodyne receiver.)
The code:
t = linspace(0, 1, 1000);
S = sin(2*pi*100*t); % Original Signal
Sc = sin(2*pi*50*t); % ‘Carrier’ Signal
HS = S.*Sc; % Heterodyne Signal
Fs = 1000;
Fn = Fs/2;
FT1 = fft(S)/length(S);
FT2 = fft(HS)/length(HS);
Fv = linspace(0, 1, fix(length(FT1)/2)+1)*Fn; % Frequency Vector
Iv = 1:length(Fv); % Index Vector
figure(1)
subplot(2,1,1)
plot(Fv, 2*abs(FT1(Iv)))
grid
subplot(2,1,2)
plot(Fv, 2*abs(FT2(Iv)))
grid
