diode_ladder_filter.hpp

// This code is released under the MIT license (see below).
//
// The MIT License
//
// Copyright (c) 2012 Dominique Wurtz (www.blaukraut.info)
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.

#ifndef __DIODE_LADDER_FILTER_HPP__
#define __DIODE_LADDER_FILTER_HPP__

#include <cmath>
#include <algorithm>

// Emulation of Diode ladder lowpass filter as found in Roland TB303 or EMS VCS3
// Version 0.1 (04/03/2012)

class DiodeLadderFilter
{
public:

    DiodeLadderFilter()
    {
        std::fill(z, z + 4, 0);
        set_q(0);
    }

    void reset()
    {
        if (k < 17) std::fill(z, z + 4, 0);
    }

    // q: resonance in the range [0..1]
    void set_q(const double q)
    {
        assert(q >= 0 && q <= 1.);
        k = 20 * q;
        A = 1 + 0.5*k; // resonance gain compensation
    }

    // Process one sample.
    //
    // x: input signal
    // fc: normalized cutoff frequency in the range [0..1] => 0 HZ .. Nyquist
    __forceinline double tick(const double x, const double fc)
    {
        assert(fc > 0 && fc < 1);
        const double wc = PI_HALF * fc; // PI is Nyquist frequency
        // wc = 2 * tan(0.5*wc); // dewarping, not required with 2x oversampling
        const double wc2 = wc*wc;
        const double wc3 = wc2*wc;
        const double wc4 = wc3*wc;
        const double b = 1 / (1+8*wc+20*wc2+16*wc3+2*wc4);
        const double g = 2*wc4 * b;

        // current state
        const double s = (z[0]*wc3 + z[1]*(wc2+2*wc3) + z[2]*(wc+4*wc2+2*wc3) + z[3]*(1+6*wc+9*wc2+2*wc3)) * b;

        // solve feedback loop (linear)
        double y4 = (g*x + s) / (1 + g*k);

        // input clipping
        const double y0 = fast_tanh(x - k*y4);

        // Compute all integrator outputs (y1, y2, y3, y4).
        // Unlike in the well-known Moog transistor ladder, this gets quite nasty due the
        // inherent coupling between filter stages.
        const double y1 = (y0*(2*wc+12*wc2+20*wc3+8*wc4) + z[0]*(1+6*wc+10*wc2+4*wc3) +
            z[1]*(2*wc+8*wc2+6*wc3) + z[2]*(2*wc2+4*wc3) + z[3]*2*wc3)*b;
        const double y2 = (y0*(2*wc2+8*wc3+6*wc4) + z[0]*(wc+4*wc2+3*wc3) +
            z[1]*(1+6*wc+11*wc2+6*wc3) + z[2]*(wc+4*wc2+4*wc3) + z[3]*(wc2+2*wc3))*b;
        const double y3 = (y0*(2*wc3+4*wc4) + z[0]*(wc2+2*wc3) +
            z[1]*(wc+4*wc2+4*wc3) + z[2]*(1+6*wc+10*wc2+4*wc3) + z[3]*(wc+4*wc2+2*wc3))*b;
        y4 = g*y0 + s;

        // update filter state
        z[0] += 4*wc*(y0 - y1 + y2);
        z[1] += 2*wc*(y1 - 2*y2 + y3);
        z[2] += 2*wc*(y2 - 2*y3 + y4);
        z[3] += 2*wc*(y3 - 2*y4);

        return A*y4;
    }

private:
    double k, A;
    double z[4];

    static __forceinline double fast_tanh(const double x)
    {
        return x / (1 + abs(x));
    }
};

#endif // __DIODE_LADDER_FILTER_HPP__