Solution:
The transfer function of the filter is given by,
H(z)=N−1∑n−0h(n)z−n=h(0)+h(1)z−1+h(2)z−2+h(3)z−3+h(4)z−4+h(5)z−5+h(6)z−6+h(7)z−7+h(8)z−8α=N−12=9−12=4.
H(z)=z−4[h(0)z4+h(1)z3+h(2)z2+h(3)z1+h(4)z0+h(5)z−1+h(6)z−2+h(7)z−3+h(8)z−4]
Since h(n)=h(N−1−n)
H(z)=z−4[h(0)(z4+z−4)+h(1)(z3+z−3)+h(2)(z2+z−2)+h(3)(z+z−1)+h(4)]
H(ω)=e−j4ω[h(0)[ej4ω+e−j4ω]+h(1)[ej3ω+e−j3ω]+h(2)[ej2ω+e−j2ω]+h(3)[ejω+e−jω]+h(4)]=e−j4ω[h(4)+23∑n=0h(n)cos(4−n)ω]=e−j4ω|H(ω)|
where |H(ω)| is the magnitude response and θ(ω)=−5ω is the phase response. The phase delay τp and group delay τg are given by
τp=−θ(ω)ω=5 and τg=d(θ(ω))dω=−d(−5ω)dω=5