4 The first Matlab figure below with four subplots are time

4) The first Matlab figure below with four subplots are time functions that are to be convolved; each subplot of the second Matlab figure is the result of convolving two of the functions from the first figure. Identify the two signals convolved for each of the four subplots of the second figure.

Solution

Convolution:-

Convolution is a mathematical operation used to express the relation between input and output of an LTI system. It relates input, output and impulse response of an LTI system as y(t)=x(t)h(t)

Where y (t) = output of LTI

x (t) = input of LTI

h (t) = impulse response of LTI

Continuous Convolution

y(t)=x(t)h(t)y(t)=x(t)h(t)

=x()h(t)d=x()h(t)d

(or)

=x(t)h()d=x(t)h()d

Discrete Convolution

y(n)=x(n)h(n)y(n)=x(n)h(n)

=k=x(k)h(nk)=k=x(k)h(nk)

(or)

=k=x(nk)h(k)=k=x(nk)h(k)

By using convolution we can find zero state response of the system.

Matlab Code For Convolution