Elimination of for loops

I am learning how to optimize code in MATLAB.

I have the following mathematical experession, where is a unit pulse of length T, and is a constant.

I am looking to eliminate the for loops for n and l but I am struggling with how to apply the unit pulse.

Would welcome any input folks may have.

[Rik]

If you post the working code for your nested loop, it should be a lot easier to vectorize your code.

Note that it might not actually be faster, as Matlab for loop are quite efficient, and large ndgrid arrays could need the pagefile to fit into the memory.

[Bruno Luong]

What exactly is a "unit pulse of length T"?

In other word how do you compute sp(t) for a given t in MATLAB?

[Howard Wilton]

Sorry, here is the definition, .

[Bruno Luong]

Then if I'm mot mistaken you don't need any loop at all. For given t

• There is at most only one l that make sp(t-lT) = 1. The inner sum has only one term that is not 0.
• The outer term is a sum of geometric series, you have a formula for it.

Answer 1

[Matt J]

L=2;
T=1;
w0=2*pi;
N=3;

ts=linspace(0,T,101)'; ts(end)=[];
w=w0+(0:N-1)/T;

s=repmat(sum(exp(1j*ts*w) ,2).',1,L);

Answer 2

[Bruno Luong]

L=2;
T=1;
w0=2*pi;
N=3;

% Any t as you like without restriction
t = linspace(0,L*T,500);

l = floor(t / T);
dt = mod(t, T); % dt = t-lT
s = exp(1j*dt.*w0).*(1-exp(1j*dt*N/T))./(1-exp(1j*dt/T));
s(l < 0 | l >= N) = 0; % inner sum has 0 term for these conditions

plot(s)