Frequency response and Impulse Response

Cossie

Im struggling to do the following question. Any help would be appreciated

A following system has the following difference equation

y(n)+ 1/8y(n-1) - 5/8y(n-2)=1/2x(n-1)

First part is to calculate the system transfer function using the z transform. Then get the frequency response and the impulse

Ive managed to work out the system function and using the z transform it equates to
[itex]\frac{Y(z)}{X(z)}[/itex]=[itex]\frac{1/2z^{-1}}{1+1/8z^{-1}-5/8z^{-2}}[/itex]

From this how do i calculate the frequency response and the impulse response of the system.

Many thanks
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

rude man

What is the z transform of δ(t), the Dirac delta (impulse) step function?

What is the relationship between a network's impulse response and its frequency response?
(Either in the s or z domain?).