Plotting a rectangular pulse with a exponential under the rectangular pulse

Hello,

I am trying to create a MATLAB Simulation that uses this equation:

s(t) = A*rect(t/tau)*exp(j*w*t); where w = 2*pi*f and f = 3 GHz

Then I am looking to I am looking to create another MATLAB Simulation using this equation:

s(t)= [rect((t-to)/tau)+ rect((t+to)/tau)]*exp(j*w*t)

but if possible I need the second equation to have the same amount of energy as the first equation.

Therefore, the second equation will be skinnier, but have a higher amplitude to compensate for the energy lost.

Any help would be greatly appreciated.

Thank you!

Answer 1

[Image Analyst]

How about starting like this:

f = 3 % GHz
w = 2*pi*f
tau = 9; % Whatever...
t = 1 : 500; % Whatever...
A = 40; % Whatever...
s1 = A*rect(t/tau)*exp(j*w*t); 
plot(t, s1, 'b-');
grid on;
s2 = [rect((t-to)/tau)+ rect((t+to)/tau)]*exp(j*w*t)

s1Area = sum(.....
s2Area = sum(.....
s1 = s1 / s1Area;
s2 = s2 / s2Area;