$8.$ An FIR filter impulse response can be found through windowing as h$($n$)=$ hd$($n$)$w$($n$).$

$($a$)$ Give an expression for H$($ejw

$)$ in terms of Hd$($ejw

$)$ and W$($ejw

$).$

$($b$)$ Find h$($n$)$ in terms of hd$($n$)$ if P is even and

$($c$)$ How many coefficients does h$($n$)$ have $?$

$($d$)$ What kind of phase is H$($ejw

$)$ likely to have $?($ linear or zero$)$