The desired plot will be obtained when N, the number of elements of t, is an integer multiple of the ratios Fs/Fn, where Fs is the sample frequency and Fn are the frequencies in Vs (in Hz). In this case we have
Fs = 200;
Fn = [20 60];
Given these vaues, selecting N = k*100 will satisy the criterion:
syms k N
N = k*sym(100);
N*sym(Fn)./sym(Fs) % integer valued for all integer k
Here is the "good" case in the question:
N = 2800;
N.*Fn./Fs % integer
tfinal = func(N,Fs,Fn)
Here is another case, where N satisfies the criteria, but is not a muliple of 100
N = 2820;
N.*Fn./Fs % integer
tfinal = func(N,Fs,Fn)
As you already showed, choosing N = 2801, which does not satisfy the criterion, results in an undesired plot
N = 2801;
N.*Fn./Fs % not both integers
tfinal = func(N,Fs,Fn)
Note this result is not wrong. It is correct based on the input parameters.
function tfinal = func(N,Fs,Fn)
t = (0:(N-1))/Fs;
Vs = 10*cos(2*pi*Fn(1)*t-pi/5)+13*cos(2*pi*Fn(2)*t+pi/6);
Spectrum = fft(Vs)/length(Vs);
Spectrum(2:end-1) = Spectrum(2:end-1)*2;
Amplitude = abs(Spectrum);
Phase = angle(Spectrum);
figure;
stem((0:N-1)/N*Fs,Amplitude)
xlim([0 Fs/2])
xlabel('Hz')
tfinal = t(end);
end
