# Elimination of for loops

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Howard Wilton on 17 Nov 2022
Edited: Bruno Luong on 17 Nov 2022
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.
Howard Wilton on 17 Nov 2022
Sorry, here is the definition, .
Bruno Luong on 17 Nov 2022
Edited: Bruno Luong on 17 Nov 2022
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.

Matt J on 17 Nov 2022
Edited: Matt J on 17 Nov 2022
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);

Bruno Luong on 17 Nov 2022
Edited: Bruno Luong on 17 Nov 2022
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)

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