I am hoping someone can give me some advice with where to start answering the folloing question.

The transfer function for a resonance filter is

\(H(z) = \frac{(1-r)(1-rz^2)}{1 - 2r cos(\omega_{c}T)z^-1 + r^2 z^-2}\)

How do I Show that, for any given resonance frequency !c and any value of the parameter r, the amplitude response of the filter equals unity at \(\omega = \omega_{c} = 2\pi f_{c}\), i.e. \(|H(\omega_{c}| = 1\).

Any advice would be great.

Thanks in advance.

Seán