[PD] EQs - FIR or Biquad or others

[Mathieu Bouchard]

On Fri, 23 Dec 2005, c wrote:

> sqrt(pow(($b0+$b1*cos($w)+$b2*cos(2*$w)),2)+pow(($b1*sin($w)+$b2*sin(2*$w)),2))/sqrt(pow(($a0+$a1*cos($w)+$a2*cos(2*$w)),2)+pow(($a1*sin($w)+$a2*sin(2*$w)),2))

This scary-looking formula is less scary reformatted like this:

sqrt(pow(($b0+$b1*cos($w)+$b2*cos(2*$w)),2)
    +pow((    $b1*sin($w)+$b2*sin(2*$w)),2))/
sqrt(pow(($a0+$a1*cos($w)+$a2*cos(2*$w)),2)
    +pow((    $a1*sin($w)+$a2*sin(2*$w)),2))

And then using slightly more advanced math concepts it can be further
simplified like this:

norm(($b0,0)+($b1,$b2)*M)/
norm(($a0,0)+($a1,$a2)*M)
where M is the matrix
  (cos($w), cos(2*$w);
   sin($w), sin(2*$w))

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| Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
| Freelance Digital Arts Engineer, Montréal QC Canada