Signals and Systems

SHORT QUESTIONS AND ANSWERS

 

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:         x₁(T)*x₂(t) = x₂(t)*x₁(t)

Associative property:      x₁(t)*[x₂(t) *x₃(t)] = [x₁(t)*x₂(t)] *x₃(t)