The frequency response of a filter is H $($e j $)=1\mathrm{.}5+$ cos$(2$$),$ $$ $$ $.$

$($a$)$ Is $|$H $($e j $)|=$ H $($e j $)?$ Is phase zero?

$($b$)$ Find the impulse response h$[$n$]$ of this filter. What type of filter is it$?$ FIR? IIR? Is it

causal? Explain.

$($c$)$ Let H$1($e j $)=$ e$$j N H $($e j $)$ determine the value of the positive integer N so that

H$1($e j $)$ has linear phase. Use the impulse response h$[$n$]$ found above to find the im$-$

pulse response h$1[$n$].$