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

Properties of linear convolution:

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*)

Distributive Property: *x*_{1}(*t*)*[*x*_{2}(*t*) + *x*_{3}(*t*)] = *x*_{1}(*t*)**x*_{2}(*t*) + *x*_{1}(*t*) **x*_{3}(*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*).

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 ...

Start Free Trial

No credit card required