[PD] bandpass makeup gain formula?

[Peter P.]

* Miller Puckette via Pd-list <pd-list at lists.iem.at> [2020-03-04 16:49]:
> vcf~ aims for an approximate peak gain of 1 (although this is _very_
> approximate for low values of Q).
Thanks for the info Miller!

Measuring vcf~ with a Q of 5 and noise~ I do get different results
depending on the center frequency. For 100Hz the filter output is
26dBRMS softer than its input signal, at 1000Hz it is 16dBRMS softer,
and at 10000Hz it is 5dB softer. Raising the Q to 15 softenes all three
levels accordingly.
 
> Me, I use Q+1 to normalize filtered white noise.  
Is that the way how you do it in vcf~'s code or how you would do it to
normalize after bp~?

> But theory would suggest
> the output power should be proportional to bandwidth (= f/Q) - with the
> bandwidth limited to Nyquist frequency - so one would divide by
> sqrt(min(f/Q, SR/2)) . I'll stick with multiplying by Q+1 for myself :)
I can't seem to get around the fact that sqrt(f/Q) changes with center
frequency, and Q+1 does not. Is that part of the simplification?´

Shouldn't the bandwidth of the filter let the same signal enery pass
regardless of center frequency?

Sorry if I skipped this part of my DSP classes...

thanks!
P