GATE 2024 Signals & Systems Foundation Quiz 96

The z-transform of a signal x[n] is given by .
If X(z) converges on the unit circle, x[n] is

Find the value of x(n) at n = 0 if x(n) is a absolutely integrable signal and

The z transform of  is

The discrete time signal x(n), the Z transform is defined as X(z). If x(n) is defined as

Then the value of X (1) is

The region of convergence of a signal x[n] whose z-transform is represented as X(z), where