MATLAB: How to implement a sum of square pulses encoding a data message

binary messagebitstreamrectangularpulse

I want to create a function m(t) such that
m(t) = a_0*p(t) + a_1*p(t-T) + a_2*p(t-2T) … + a_n*p(t-2N)
ie, m(t) = sum(a_kp(t-kT))
where
-T defined by user
-a_k coefficients in binary, defined by user
The plot of m(t) against time should therefore be pulses of width T representing a bitstream corresponding to what was entered by the user.
Right now I'm only concerned with p(t) as rectangular pulse.
I've tried several ways of implementing this and I always get stuck at trying to define the pulse train successfully. Is there not a simple way of shifting rectangularPulse(a,b,t) and adding it to itself? I'm not very familiar with Matlab and I think all the vector stuff is messing me up.

Best Answer

You can use functions from Symbolic Math Toolbox for achieving what you are trying to do. The "rectangularPulse" pulse function can help you create the "p(t)" function.
You may find the following MATLAB script helpful to get started:
syms t % create the time variable
N = 10; % number of time points
T = 1; % Time period for the pulse
a = rand(1,N); % example values 
m = 0; % the function which you are trying to create
for k = 1:N
    m = m + a(k)*rectangularPulse(-k*T,-(k-1)*T,t);
end
fplot(m,[-11 1])
I hope this helps.
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