Discrete Convolution Attempt

Question 1 The following information is known about a linear, time-invariant system: •

The system is causal

•

When the input is:

The z-transform of the output is

a) Find the z-transform of x(n)

b) What are the possible choices for the region of convergence of Y(z) and what are the properties of the associated system? There are two poles, at ½ and at 2. Thus there are three regions of convergence. Left Sided Sequence, Acausal, Unstable Right Sided Sequence, Causal, Unstable Two sided Sequence, Acausal, Stable

c) What are the possible choices for the impulse response of the system?

d) Assuming that the system is casual, find the output y(n) by computing the inverse z-transform of Y(z). Verify your result by computing the convolution between the input and the impulse response of the system.

Solve either by long division or by partial fractions