Question

Find inverse z transform of X˜(z) = z(4z − 2) 3z 2 − 4z + 1

Answer 1

To find the inverse z-transform of X˜(z) = z (4z − 2) / (3z^2 − 4z + 1), use partial fraction decomposition and take the inverse z-transform of each term.

Step-by-step explanation:

To find the inverse z-transform of X˜(z) = z (4z − 2) / (3z^2 − 4z + 1), we can use partial fraction decomposition.

We can rewrite the expression as X˜(z) = (2z^2 - z) / (3z^2 − 4z + 1) + 1 / (z - 1).

Using partial fraction decomposition and taking the inverse z-transform of each term,

X(n) = 2(n - 1) U (n - 1) - (1/2) ^n + (1) ^n, where U(n) is the unit step function.