Signals and Systems

SIGNIFICANT POINTS

 

The convolution of x(t) with h(t) is defined by

 

 

Properties of linear convolution:

Commutative Property:         x₁(t)*x₂(t) = x₂(t)*x₁(t)

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

Distributive Property:   x₁(t)*[x₂(t) + x₃(t)] = x₁(t)*x₂(t) + x₁(t) *x₃(t)

Discrete convolution:

If the input x(n) is given to discrete time system having an impulse {h(n)}, the output is given by convolving the {h(n)} with x(n).

 

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

 

where the symbol ‘*’ represents the convolution of x(n) with h(n) and this process is also called convolution sum. It is defined by

 

 

The limits ...