Biquad Filter Transfer Function Frequency Response

Question

$H(z) = G\cdot\displaystyle\frac{2b_0\left(1-z^{-2}\right)}{1-2a_1z^{-1}-2a_2z^{-2}} + 1$

I have a data sheet with the above transfer function, I need to calculate its frequency response in code. I have the functions to calculate $b_0$, $a_1$, $a_2$ and $G$, but it has been a loooooong time since I have handled $H(z)$ transfer functions and I can't for the life of me remember how to work it out.

I have googled around and it mentions jw this and that and I have tried everything Ive found but I'm not getting a frequency response anything like what is expected.

I have a sampling rate of $48000\textrm{ Hz}$ and want to calculate the frequency response from $0-24000\textrm{ Hz}$ in $1\textrm{ Hz}$ steps.

Any help would be very much appreciated.

Answer 1

To get the frequency response, replace $z$ in $H(z)$ by $e^{j2\pi f/f_s}=\cos(2\pi f/f_s)+j\sin(2\pi f/f_s)$ where $f_s$ is the sampling frequency in Hz and $f$ is the desired frequency in Hz. This will give you the value of the frequency response at frequency $f$. Note that the frequency response is a complex function, so you might want to look at its magnitude.