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12th November 2011, 08:45 PM  #1 
diyAudio Member
Join Date: Mar 2007
Location: California

advanced biquad programming: how to set gain for each biquad?
I am developing some tools for calculating the IIR transfer function coefficients for the biquads in the MiniDSP. So far I have successfully figured out how to calculate the coefficients for first and second order filter functions and a "gain block" (e.g. b0=gain, all other coefficients=0). I developed my calcs using some of the "cookbook" type of documents that are floating around the web.
The one thing I can not seem to figure out, is how to have a filter with a gain of than unity implemented together in the same biquad. I know in analog filter transfer functions I can just multiple the numerator coefficients by the voltage gain that I want to use, and that does the trick. This does not seem to work for an IIR filter. For example, in a single biquad, I want to describe a 2nd order high pass filter with Q=0.7071, corner frequency 500Hz, and voltage gain of 0.707. How to I include the over all biquad gain in my coefficient calculations? I'd like to know a general way to do this for any first or second order filter function. Thanks in advance. Charlie 
14th November 2011, 06:59 AM  #2 
diyAudio Member
Join Date: Dec 2009

Charlie,
If you want to combine Gain (GdB) to one of your biquad filter, there is a simple way. Simply "Multiply" your numerators (all b0, b1, b2) to the linear gain value. (Glin) e.g. H(z) = Glin * (b0 + b1z1 + b2z2) / ( 1+a1z1 + a2z2) So Glin = 10^(GdB/20) Makes sense? DevTeam
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18th November 2011, 03:35 PM  #3 
diyAudio Member
Join Date: Mar 2007
Location: California

Thanks for your reply. You are correct.
I discovered my mistake: in the nomenclature I was following, the numerator coefficients of the transfer function are denoted b0, b1, b2 for IIR filters but are denoted a0, a1, a2 for analog filters. I was just multiplying the wrong set of coefficients! Charlie 
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