Consider a system is described by

$y(n)=3x(n)+4x(n-1)-2y(n-1).$

Using z$-$transform, find the inverse of this system in the time domain.

Solution:

Given that the impulse response of the system is $h(n),$ then finding the system inverse is equivalent to finding $g(n)$ such that

$h(n)**g(n)=(n)$

and in the frequency domain, this is represented as

$H(z)G(z)=1$