Help implementing digital filter from tansfer function I'm trying to implement a digital filter, which is given by the following transfer function:
$$
1+2V K \frac{K+c_m+2Kz^{-1}+(K-c_m)z^{-2}}{1+2Kc_m+K^2+(2K^2-2)z^{-1}+(1-2Kc_m+K^2)z^{-2}} 
$$
$$
+V^2K^2\frac{1+2z^{-1}+z^{-2}}{1+2Kc_m+K^2+(2K^2-2)z^{-1}+(1-2Kc_m+K^2)z^{-2}}
$$
My interpretation of the coefficients is this:
$a0_1 =  1+2V K$
$a1_1 =  2Kc_m+K^2+(2K^2-2)$
$a2_1 = (1-2Kc_m+K^2)$
$b0_1 = K+c_m$
$b1_1 = 2K$
$b2_1 = K-c_m$
$a0_2 =  V^2K^2$
$a1_2 =  2Kc_m+K^2+(2K^2-2)$
$a2_2 = (1-2Kc_m+K^2)$
$b0_2 = V^2K^2$
$b1_2 = 2*(V^2K^2)$
$b2_2 = V^2K^2$
After dividing all the coefficients by a0, I try implementing them using a standard biquad:
$y[n] = b0*x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]$
in parallel, with their outputs summed.
I haven't managed to get it working. 
Am I on the right path? Is there anything I'm doing terribly wrong, or not doing? Thanks very much for any help!
You seem to do a few things wrong

Start with just transcribing each fraction, ignore the factors in front of the fraction and &quot;1&quot; in front
Make sure you sort by powers of $z$
Normalize all coefficients to $a_0$
Multiply all $b$ coefficients with the factor for the fraction.
The &quot;1&quot; is a third filter

Example
$$a0_1 = 1+2Kc_m+K^2 \\ a1_1 = 2K^2-2$$