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convolution of exponential with unit step ... using conv command

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Sadi Altamimi
Sadi Altamimi on 6 Dec 2013
Hi everybody,
Suppose we have two signals:
u(t) : unit step function and h(t) = exp(-t) * u(t)
Let us calculate their convolution. Doing that on paper is pretty easy, the result will be y(t) = (1-exp(-t)) * u(t). i.e the function will increase till it reaches the value of 1 and then it becomes constant = 1.
The big question is that why the following code produces wrong answer after time of 10s (this time is the length of the original signals)? In other words, why the result starts decaying after this time instant and reaches zero ?!
Code:
t = -1:0.01:10;
u = heaviside(t);
u(u==0.5) = 1;
subplot(221), plot(t,u), axis([-1 10 -.5 1.5])
h = exp(-t).* u;
subplot(222), plot(t,h), axis([-1 10 -.5 1.5])
C = conv(h,u)/100;
tc = [-200:length(C)-1-200]/100;
subplot(2,2,3:4), plot(tc,C), axis([-1 20 -.5 1.5])

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