[PD] bandpass makeup gain formula?

[Peter P.]

* Peter P. <peterparker at fastmail.com> [2020-03-08 18:21]:
> * 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.

I am attaching the patch I measured this with plus a small sqrt(f/Q)
calculation therein.
-------------- next part --------------
#N canvas 1121 314 729 543 12;
#X obj 98 55 noise~;
#X obj 149 143 vcf~ 0;
#X floatatom 149 244 5 0 0 3 postFilter - -;
#X floatatom 17 184 5 0 0 1 preFilter - -;
#X obj 17 337 -;
#X floatatom 17 365 5 0 0 3 difference_pre-post - -;
#X floatatom 276 76 5 0 0 0 - - -;
#X obj 258 187 *~;
#X obj 276 159 + 1;
#X floatatom 258 244 5 0 0 3 normalized - -;
#X obj 239 338 -;
#X floatatom 239 366 5 0 0 3 difference_pre-normalized - -;
#X obj 17 150 env~ 44100;
#X obj 149 214 env~ 44100;
#X obj 258 216 env~ 44100;
#X obj 42 300 t b f;
#X obj 239 286 t b f;
#X floatatom 221 77 5 0 0 0 - - -;
#X obj 605 241 /;
#X obj 620 207 t b f;
#X floatatom 618 273 5 0 0 0 - - -;
#X obj 606 299 sqrt;
#X floatatom 606 332 5 0 0 0 - - -;
#X floatatom 605 138 5 0 0 1 f - -;
#X floatatom 620 172 5 0 0 1 q - -;
#X obj 41 437 loadbang;
#X msg 41 464 \; pd dsp 1;
#X text 309 161 (Q+1) normalization;
#X msg 221 43 100;
#X msg 276 44 15;
#X obj 221 12 loadbang;
#X text 592 360 sqrt(f/q);
#X connect 0 0 1 0;
#X connect 0 0 12 0;
#X connect 1 0 7 0;
#X connect 1 0 13 0;
#X connect 2 0 15 0;
#X connect 3 0 4 0;
#X connect 3 0 10 0;
#X connect 4 0 5 0;
#X connect 6 0 1 2;
#X connect 6 0 8 0;
#X connect 7 0 14 0;
#X connect 8 0 7 1;
#X connect 9 0 16 0;
#X connect 10 0 11 0;
#X connect 12 0 3 0;
#X connect 13 0 2 0;
#X connect 14 0 9 0;
#X connect 15 0 4 0;
#X connect 15 1 4 1;
#X connect 16 0 10 0;
#X connect 16 1 10 1;
#X connect 17 0 1 1;
#X connect 18 0 20 0;
#X connect 18 0 21 0;
#X connect 19 0 18 0;
#X connect 19 1 18 1;
#X connect 21 0 22 0;
#X connect 23 0 18 0;
#X connect 24 0 19 0;
#X connect 25 0 26 0;
#X connect 28 0 17 0;
#X connect 29 0 6 0;
#X connect 30 0 28 0;
#X connect 30 0 29 0;