Most of the resources I found online go the other way. If I have the transfer function

$$ H(z) = 1 - \cos(\theta) \, z^{-1} + z^{-2} $$

How do I get the difference equation from it, so that I can apply the transfer function to a set of data?


1 Answer 1


A transfer function $H(Z)$ can be written as $H(Z)=\frac{Y(Z)}{X(Z)}$. Then, your $H(Z)$ can be written as

$\frac{Y(Z)}{X(Z)}=1-\cos\theta~Z^{-1}+Z^{-2}$ or

$Y(Z)=X(Z)(1-\cos\theta~ Z^{-1}+Z^{-2})$

Now taking the inverse $Z$transform, we get the difference equation as


I hope this help you.


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