Adding Phase shift to sum of sines

Matlab code for summation of two signals with phase shift

I am writing a code for a summation of two signals. The only part I need help in is in the addition of the phase shift which would be piecewise since it is a phase shift of three different time sections. The original problem statement is shown below that was used to create the Matlab code. The part I am stuck in is for developing the code for the phi(t) which is three different time sections. My code and plot without the phase shift are shown after the original problem statement. How do I add the phi(t) to my code. t in this case is x. Thanks in advance.

Original problem statement

My matlab code and plot without phase shift

f1 = 0.98e9;

f2 = 1.02e9;

w1 = 2*pi*f1;

w2 = 2*pi*f2;

wo = (w1+w2)/2;

wm = (w2-w1)/2;

x = 0:.05e-9:50e-9;

m = abs(20*cos(wm*x));

vo = m.*cos(wo*x);

plot(x,vo,'r')

xlabel('t')

ylabel('Vo(t)')

title('Alternative plot of two signal summation')

Answer 1

[Shoaib iqbal]

Hi Jose,

I understand that you are trying to add two sinusoids with phase shift.

You can try to make an array corresponding to phi(x), where ‘x’ is same as time steps you have specified. The total number of samples in your case is 1001 (0:0.05ns:50ns). The phi(x) is given as

Phi(x) = 0 for 0 < x < 12.5 ns

Phi(x) = pi for 12.5 ns < x < 37.5 ns

Phi(x) = 0 for 37.5 ns < x < 50 ns

12.5 ns corresponds to 251th sample, similarly 37.5 ns corresponds to 751th sample. The following code snippet creates phi(x) and Vout(x)

Phi = zeros(1,1001); 

Phi(251:750) = pi; 

Vout = m.*cos(wo*x + Phi); 

Hope this solves your query.