I need to find difference equation and frequency response

Given H(z)=(-3+z^z-1)/(1+2z^-1+3z^-2)

a) Find the difference equation

b) Plot the frequency response

[Naz]

Right. And what's your question?

Answer 1

[Walter Roberson]

Please see this previous discussion

However, it appears to me that your equation probably cannot be analyzed through these techniques, as it is not in the form of a ratio of polynomials. The z^z term is going to lead you to a lot of problems.

Answer 2

[Naz]

Difference equation (I assume that z^z-1 should be z^-1):

3y[n-2]+2y[n-1]+y[n]=-3x[n]+z[n-1]

Frequency response:

B=[-3 1];
A=[1 2 3];
[H,W] = freqz(B,A);
plot(W,H);

[Naz]

The frequency is normalized to pi

[Walter Roberson]

My speculation was that the z^z-1 should be z^2 - 1 but that doesn't make sense with the leading -3 . So I still don't know what was intended.