# [PD] biquad~ with elementary filters [was: Re: dinosaurs ...]

Charles Henry czhenry at gmail.com
Mon Sep 15 15:19:51 CEST 2008

```On Mon, Sep 15, 2008 at 7:49 AM, Damian Stewart <damian at frey.co.nz> wrote:
> dude, that's not 'easy'. i can barely remember how the quadratic formula
> works with pen and paper, let alone in C, and let alone to the point where i
> could confidently transfer from C to Pd. i'd have no idea where the bugs
> were... and indeed, no idea

Use pen and paper.  Then, take your results and make implementations
in Pd (or C, your choice).  This is a good exercise, so I'll leave it
to you to do the derivation.  I'm more than happy to help.  I do this
stuff all the time.

1. Solve for x in
a*x^2 + b*x + c =0
(use "completing the square")  This is how you derive the quadratic formula.

2. Then, solve

ff1*z^2 + ff2*z^1 + ff3 = 0
and
1*z^2 - fb1*z^1 - fb2 = 0
using the result from (1)

3.  Then, solve for fb1, fb2, ff1, ff2, ff3 in terms of the poles/zero
locations from (2)

Then, you've done all the work you need to freely exchange between
both methods.  Now, as for filter design, there's a bit more work to
do (save that for later).

Chuck

```