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## I need to find difference equation and frequency response

Asked by Noel

### Noel (view profile)

on 15 Nov 2011

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

a) Find the difference equation

b) Plot the frequency response

Naz

### Naz (view profile)

on 15 Nov 2011

Right. And what's your question?

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## 2 Answers

### Walter Roberson (view profile)

Answer by Walter Roberson

### Walter Roberson (view profile)

on 15 Nov 2011

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 by Naz

### Naz (view profile)

on 15 Nov 2011

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

### Naz (view profile)

on 15 Nov 2011

The frequency is normalized to pi

Walter Roberson

### Walter Roberson (view profile)

on 15 Nov 2011

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.

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