Calculate convolution of two given continuous signals in matlab

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Chihiro Ogino 2022-5-26

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https://ww2.mathworks.cn/matlabcentral/answers/1727510-calculate-convolution-of-two-given-continuous-signals-in-matlab

评论： Chihiro Ogino 2022-6-11

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)

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Answer 1

Paul 2022-6-5

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https://ww2.mathworks.cn/matlabcentral/answers/1727510-calculate-convolution-of-two-given-continuous-signals-in-matlab#answer_979365

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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')