[PD] bandpass makeup gain formula?

[Alexandre Torres Porres]

I've done a nice job plotting the frequency response of both bp~ and vcf~
and exposing their formulas,

see
https://github.com/porres/Live-Electronics-Tutorial/tree/v1.0-beta-17/Examples/Vol.2/Part.05-Filters(Basic)/22-Filters.types/2.Filter.Types/2.Resonant/2.Bandpass

and
https://github.com/porres/Live-Electronics-Tutorial/tree/v1.0-beta-17/Examples/Vol.2/Part.09-Filters-Reverb-Karplus/31-Filters(Advanced)/3.Z-plane

Em dom., 8 de mar. de 2020 às 19:59, Miller Puckette via Pd-list <
pd-list at lists.iem.at> escreveu:

> >
> > 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.
> >
> Aha - yes, my (Q+!) fix aims to allow changing Q without much affecting
> the perceived loudness, but doesn't account for varying the center
> frequency.
>
> To loudness-balance filtered white noise, you'd want to aim to get the
> same signal power as the noise has in a one-bark-wide band.  Above 500Hz
> this increases linearly with frequency.  So you'd want a 10-dB increase
> in the signal for a 10x increase in center frequency.  However, for
> frequencies
> below 500hz you'd want the result to be roughly independent of center
> frequency.  So what you're seeing looks OK except that it should be
> corrected
> below 500 Hz.
>
> OTOH if you want to balance with the whole of the white-spectrum noise (not
> just the slice that's in your local bark) then you have to go look at
> equal-loudness coutours (since in that case we're comparing loudnesses of
> sounds at different frequencies).  At that point I just give up and use my
> ears :)
>
> > > 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~?
> >
> That's how I normalize in the patch.  Example (but ignore the Hilbert
> stuff):
>
> http://msp.ucsd.edu/syllabi/171.20w/patches/7.e.graphing-resonant-filter.pd
>
> > > 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?
> >
> Yeah, depends on whether you want to match power ( roughly dividing by
> sqrt(f/Q) for "reasonable" f/Q values) or "sound good" (as I think Q+1 does
> fairly well).
>
> Also, the result for white noise isn't necessarily representative of what
> you
> get filtering real signals - all sorts of things happen then.
>
> cheers
> Miller
> > Sorry if I skipped this part of my DSP classes...
> >
> > thanks!
> > P
> >
> >
> >
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