# Solve: Communications Systems

A discrete time system is described by the following transfer function:

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

a) Give a block diagram to implement the system using delay elements, multipliers, and adders. Use the smallest possible number of delay elements (all of the same delay).

b) Find the impulse response of the system.

c) Give a different equation, in terms of the input and output, to describe the system.

d) Is the system stable?

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#### Solution Preview

H(Z) = [1+2z(^-1)]/[1-(1/2)z^(-2)]

1. See the attached file for the block diagram

2. Impulse response:

h(z) = [1+2z^(-1)]/[1-(1/2)z^(-2)]

Multiply both numerator and denominator by z^2 h(z) = [z^2+2z]/[z^2 -(1/2)

= z(z+2)/[{z+(1/2^0.5)}*{z-(1/2^0.5)}]

Now we need to get h(n), the impulse response.

We need the inverse z-transform ...

#### Solution Summary

This response provides step-by-step calculations to solve each of the questions, as well as an attached .bmp file with a block diagram.