Calculate convolution of two given continuous signals in matlab

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If I have two continuous signals ,f1(t) = g10(t) and f2(t) = (e^-t)*u(t). How can I calculate the convolution and plot the graph for that? N:B: here g10 means the width of rectangular is 10(eg: -5 to 5)

Accepted Answer

Paul on 5 Jun 2022
Closed form solution using symbolic math
syms t tau real
f1(t) = rectangularPulse(-5,5,t);
f2(t) = exp(-t)*heaviside(t);
y1(t) = int(f1(tau)*f2(t-tau),tau,-5,t)
y1(t) = 
fplot(y1(t),[-10 10])
hold on
Numerical solution using integral()
f1 = @(t) abs(t) <= 5;
f2 = @(t) exp(-t).*(t>=0);
y2 = @(t) integral(@(tau)(f1(tau).*f2(t-tau)),-5,t);
for tval = -7:2:10
Numerical solution using conv(). Note that we have to settle for a vaue of t where we are willing to accept f2(t) = 0
dt = 0.1;
tval = -5:dt:15;
y3 = conv(f1(tval),f2(tval))*dt;
conv() assumes that the sequences start at t = 0, so we have to shift our time reference left by 5. Make dt smaller to improve the convolution sum approximation.
legend('Closed Form','integral()','conv()','Location','NorthWest')

More Answers (1)

Paul on 27 May 2022
Assuming a closed form solution is desired this problem can be solved with the Symbolic Math Toolbox
and also exp() (no doc page for Symbolic Math Toolbox version?)
Paul on 28 May 2022
Then I guess you'll have to either do it by hand (or use other s/w that can do it symbolically), or you can use
to compute a numerical approximation of the convolution integral, or can use
to compute a numerical approximation to the convolution integral via the convolution sum.

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