Given the z-transform pair,

x [n] →X (z) =(z^-1)/(1+0.8z^-1) with ROC: |Z| > 0.8

use the z-transform properties to determine the z-transform of the following sequences:
a) y[n] = x[n+2]

b) y[n] = (5/4)n x[n]

c) y[n] = (n+1) x[n-1]

d) y[n] = x[n] * x[2-n] (* represents convolution)

PROBLEM 2

a) A system has the transfer function

H(z) =(z^-1)/(1+4z^-2)

We know that the system is causal. Is it stable? Why?

b) A system has two poles:

p1 = -0.32, p2 = 0.6

-Its region of convergence is ROC: 0.6 < |z| < 2. Is it stable? Is it causal? Why?

PROBLEM 3

Consider a causal LTI system described by the difference equation:
y[n] = y[n-1] + y[n-3] + x[n-2]

with initial conditions:

y[-1] = 1, y[-2] = 0, y[-3] = -1.

x[-1] = 2, x[-2] = 1, x[-3] = 5

-What is the one-sided z-transform of y[n]?