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.
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 + b1z-1 + b2z-2) / ( 1+a1z-1 + a2z-2)
So Glin = 10^(GdB/20)
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!
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