I need to design a number of digital IIR filters based upon transfer functions given in the s-domain. I have applied the bilinear transform to give the transfer functions in the Z-domain, however I need to expand and simplify the equations to place them in the form below:

Attachment 6961

Once the equations are in the above form I can get the IIR filter coefficients and implement them into my filters, however I'm not quite sure how to go about it. Would anybody like to take a crack for me?

The three equations are as follows;

1. Attachment 6960

2. Attachment 6962

3. Attachment 6963

An example is given below;

Attachment 6965

Any help would be very much appreciated!