1) Find the z-transform x(z) of x(n) = cos(0.45n +0.25)u(n).
2) Find the system transfer function of a causal LSI system whose impulse response is given by
h[n] = (-0.5)^n-1 sin[0.5(n-2)]u[n-2] and express the result in positive powers of z. Hint: The transfer function is just the z-transform of impulse response. However, we must first convert the power of -0.5 from (n - 1) to (n - 2) by suitable algebraic manipulation.
3) Express the following signal, x(n), in a form such that z-transform tables can be applied directly. In other words, write it in a form such that the power of 0.25 is (n-1) and the argument of sin is also expressed with a (n-1) multiplier.
x[n] = (0.25)^n sin(pi/2 n) u [n-1]
4) The transfer function of a system is given below. Find its impulse response in n-domain. Hint: First expand using partial fraction expansion and then perform its inversion using z-transform tables
H(z) = 1/(z-0.5)(z+0.5)
5) The transfer function of a system is given by
H(z) = z/(z^2-0.8z+0.15)