Filters 1-pole with faked resonance

filter1PoleResonant.dsp

import("stdfaust.lib");

///
lp1Reson(cutoff, dbGain, cfSmooth) = lp : peak with {
  lp = fi.iir((1-p),(0-p)) with {
    p = exp(-2.*ma.PI*cutoff/ma.SR) : cfSmooth;
  };
  peak = fi.tf22t(b0/a0,b1/a0,b2/a0,a1/a0,a2/a0) with {
    w = max(0,cutoff)*(2*ma.PI/ma.SR);
    A = 10^(dbGain/40);
    S = sin(w) : cfSmooth; C = cos(w) : cfSmooth;
    b0 = 1+S*A; b1 =-2*C; b2 = 1-S*A;
    a0 = 1+S/A; a1 =-2*C; a2 = 1-S/A;
  };
};

hp1Reson(cutoff, dbGain, cfSmooth) = lp : peak with {
  lp = fi.iir((0.5*(1.+p),-0.5*(1+p)),(0.-p)) with {
    p = exp(-2.*ma.PI*cutoff/ma.SR) : cfSmooth;
  };
  peak = fi.tf22t(b0/a0,b1/a0,b2/a0,a1/a0,a2/a0) with {
    w = max(0,cutoff)*(2*ma.PI/ma.SR);
    A = 10^(dbGain/40);
    S = sin(w) : cfSmooth; C = cos(w) : cfSmooth;
    b0 = 1+S*A; b1 =-2*C; b2 = 1-S*A;
    a0 = 1+S/A; a1 =-2*C; a2 = 1-S/A;
  };
};

///
process =
  //par(i, 2, lp1Reson(cutoff, pkShGain, cfSmooth))
  par(i, 2, hp1Reson(cutoff, pkShGain, cfSmooth))
with {
  cfSmooth = si.smooth(ba.tau2pole(50e-3));
  cutoff = hslider("[01] Cutoff [unit:Hz] [scale:log]", 440.0, 50.0, 10000.0, 1.0) : max(1.0) : min(20000.0);
  pkShGain = hslider("[02] Peak/shelf gain [unit:dB]", 0.0, 0.0, 40.0, 0.1) : max(-120.0) : min(60.0);
};