Calculate convolution of two given continuous signals in matlab

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)

Answer 1

[Paul]

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) = 

figure;
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
    plot(tval,y2(tval),'rx')
end

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.

plot(tval-5,y3(1:numel(tval)),'ko')
legend('Closed Form','integral()','conv()','Location','NorthWest')

[Chihiro Ogino]

A pretty clear explanation it is! Much thanks

Answer 2

[Paul]

Assuming a closed form solution is desired this problem can be solved with the Symbolic Math Toolbox

syms

rectangularPulse

int

heaviside

and also exp() (no doc page for Symbolic Math Toolbox version?)

[Chihiro Ogino]

But it shows that I've no Symbolic Toolbox. This is my very first tme using Matlab , and I'm totally lost how to overcome the issues

[Paul]

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

integral

to compute a numerical approximation of the convolution integral, or can use

conv

to compute a numerical approximation to the convolution integral via the convolution sum.