Reference no: EM13249456

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-1sin[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)(z0.5)

5. The transfer function of a system is given by

H(z) = Z/(z^2-0.8z+0.15)

To such a system we apply an input of the type x[n[= e^-0.4n for n>= 0.