$5\mathrm{.}12$ Consider the filter, y$($n$)=0\mathrm{.}9$y$($n$-1)+$bx$($n$),($a$)$ determine b so that $|$H$(0)|=1.($b$)$ Determine the frequency at which $|$H$($w$)|=1/$squa$(2).($c$)$ Is this filter lowpass, bandpass, or highpass? $($d$)$ Repeat parts $($b$)$ and $($c$)$ for the filter y$($n$)=-0\mathrm{.}9$y$($n$-1)+0\mathrm{.}1$x$($n$)$