how to implement a sum of square pulses encoding a data message

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.

Answer 1

[Jayaram Theegala]

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.

[musedpony]

Thank – yes, that worked! I used this:

syms t % create the time variable

%user input time duratio no pulses p(t) x = inputdlg('Enter the time duration for each pulse'); T = str2double(x{:});

%define binary input as coefficients for message of shifted pulses binaryMess = inputdlg('Enter an 8-bit space-separated binary sequence for transmission:',... 'Sample', [1 50]); a = str2num(binaryMess{:}); N = length(a);

m = 0; % define the function m(t)

%implement m(t) as a sum of shifted rectangular pulses with coefficients a, %duration T for k = 1:N m = m + a(k)*rectangularPulse((k-1)*T,k*T,t); end

%plot message fplot(m,[0 N*T+T])