$[$Problem $2](30$ points$)$ Answer the following questions about the system whose Z$-$transform system function is

$H(z)=\frac{1+z^{-1}}{1-0\mathrm{.}9z^{-1}}$

$($a$)$ Draw the amplitude of frequency response roughly from the locations of the poles and zeros.

$($b$)$ Find the impulse response of this system.

$($c$)$ Obtain the output sequence of this system to the input represented by

$x[n]=2*cos(2n+\frac{}{4})*u[n]$