**Q1**. Define the convolution of *x*(*t*) with *h*(*t*).

**Ans.:** The convolution of *x*(*t*) with *h*(*t*) is defined by

Hence the output *y*(*t*) is the convolution of *h*(*t*) and *x*(*t*).

∴ (*y*) = Convolution of *h*(*t*) and *x(t)* =*x(t)* ^{*} *h(t)* =

The symbol ‘*’ in Eq. (7.2) stands for convolution.

**Q2.** State the properties of linear convolution.

**Ans.:** The linear convolution possesses the following properties:

Commutative property: *x*_{1}(*T*)**x*_{2}(*t*) = *x*_{2}(*t*)**x*_{1}(*t*)

Associative property: *x*_{1}(*t*)*[*x*_{2}(*t*) **x*_{3}(*t*)] = [*x*_{1}(*t*)**x*_{2}(*t*)] **x*_{3}(*t*)

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