The error in the following code:
F0 =13; T0 =1/F0; Ts = 0.07; t = 0:Ts:13*T0; x = real(exp(j*(2*pi*F0*t-pi/2))); plot(t,x)
is the value for Ts is too large. The sampling frequency needs to much smaller to get a good result.
If we change the value to 1/2000 the code will work as expected.