LTI-filter, compute H(z) from freqz-response

[mkkribor]

Hi!

I have a problem i can't solve:

Compute the System Function H(z) from the Frequency

H(e^jw)=2e^(-j 3/2 w) 〖[cos(w/2)]〗^2


The answer should be in the form:
H(z)= (b_0+b_1 z^(-1)+b_2 z^(-2)+⋯)/(1-a_1 z^(-1)-a_2 z^(-2)-…)
where z = e^jw, and the b and a are constants.

Thx for any help!

 

[mkkribor]

I get to the point where:

H(e^[jw]) = e^[-j(w/2)] * (1 + 2e^[-jw] + e^[-j2w])

but then I am stuck..