Biquad frequency response again

[robert bristow-johnson]

>Greetings,
>
>A little while ago I posted a question about how to calculate the frequency
>response of a biquad filter.
>
>someone pointed me to the excellent reference at
>http://www.brokersys.com/~jmac/dsp/fresp.html It provides C code for
>calculating the response curve of a given set of filter coeficients. The
>only problem is that it requires a0 to be 1.0, and I'd like to use it to
>calculate curves for Robert Bristow-Johnson's cookbook formulae, which don't
>have a0 set to 1.0.
>
>My question is:
>Is there a simple way to fudge the coefficients to guarantee a0 == 1.0?

YES!  (and it's in the post as well as a typical system theory text.)  you
do the old multiply and divide by the same quantity trick.  you can
multiply the top and bottom of the transfer function by any non-zero number
you want (and it changes _nothing_).  how about multiplying top and bottom
by 1/a0?

BTW, the _magnitude_ frequency response is:

sqrt[(b0+b1*cos(theta)+b2*cos(2*theta))^2+(b1*sin(theta)+b2*sin(2*theta))^2]/
sqrt[(a0+a1*cos(theta)+a2*cos(2*theta))^2+(a1*sin(theta)+a2*sin(2*theta))^2]

have phun.



r b-j
pbjrbj at viconet.com   a.k.a.   robert at audioheads.com
                     a.k.a.   robert at wavemechanics.com

"Don't give in to the Dark Side.  Boycott intel and microsoft."