Moog VCF

  • Author or source: CSound source code, Stilson/Smith CCRMA paper.
  • Type: 24db resonant lowpass
  • Created: 2002-01-17 02:02:40
notes
Digital approximation of Moog VCF. Fairly easy to calculate coefficients, fairly easy to
process algorithm, good sound.
code
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//Init
cutoff = cutoff freq in Hz
fs = sampling frequency //(e.g. 44100Hz)
res = resonance [0 - 1] //(minimum - maximum)

f = 2 * cutoff / fs; //[0 - 1]
k = 3.6*f - 1.6*f*f -1; //(Empirical tunning)
p = (k+1)*0.5;
scale = e^((1-p)*1.386249;
r = res*scale;
y4 = output;

y1=y2=y3=y4=oldx=oldy1=oldy2=oldy3=0;

//Loop
//--Inverted feed back for corner peaking
x = input - r*y4;

//Four cascaded onepole filters (bilinear transform)
y1=x*p + oldx*p - k*y1;
y2=y1*p+oldy1*p - k*y2;
y3=y2*p+oldy2*p - k*y3;
y4=y3*p+oldy3*p - k*y4;

//Clipper band limited sigmoid
y4 = y4 - (y4^3)/6;

oldx = x;
oldy1 = y1;
oldy2 = y2;
oldy3 = y3;

Comments

I guess the input is supposed to be between -1..1

Still working on this one. Anyone notice it's got a few syntax problems? Makes me wonder if it's even been tried.

Missing parenthesis. Uses ^ twice. If I get it to work, I'll post usable code.

                        OK. Can't guarantee this is a 100% translation to real C++, but it does work. Aside from possible mistakes, I mucked hard with the coefficient translation, so that there is a slight difference in the numbers.

1. What kind of filter ends up with exp() in the coefficient calculation instead of the usual sin(), cos(), tan() transcendentals? If someone can explain where the e to the x comes from, I'd appreciate it.

2. Since I didn't understand the origin of the coefficients, I saw the whole section as an excercise in algebra. There were some superfluous multiplications and additions.

First I implemented the e to the x with pow(). That was stupid. I switched to exp(). Hated that too. Checked out the range of inputs and decided on a common approximation for exp().

I think it's now one of the fastest filter coefficient calcs you'll see for a 4 pole. Go ahead--put the cutoff on an envelope and the q on an LFO. Hell, FM the Q if you want!

A pretty good filter. Watch the res (aka Q). Above 9, squeals like a pig. Not in a good way.

Needs more work, i think, to stand up with the better LPs in the real VST world. But an awfully cool starting place.

If I did something awful here in the translation, or if you have a question about how to use it, best to ask me (mistertoast) over at KvRaudio.com in the dev section.

I'm toying with the idea of wedging this into TobyBear's filter designer as a flt file. If you manage first, let me know. I'm mistertoast.

MoogFilter.h:

class MoogFilter
{
public:
MoogFilter();
void init();
void calc();
float process(float x);
~MoogFilter();
float getCutoff();
void setCutoff(float c);
float getRes();
void setRes(float r);
protected:
float cutoff;
float res;
float fs;
float y1,y2,y3,y4;
float oldx;
float oldy1,oldy2,oldy3;
float x;
float r;
float p;
float k;
};

MoogFilter.cpp:

#include "MoogFilter.h"

MoogFilter::MoogFilter()
{
fs=44100.0;

init();
}

MoogFilter::~MoogFilter()
{
}

void MoogFilter::init()
{
// initialize values
y1=y2=y3=y4=oldx=oldy1=oldy2=oldy3=0;
calc();
};

void MoogFilter::calc()
{
float f = (cutoff+cutoff) / fs; //[0 - 1]
p=f*(1.8f-0.8f*f);
k=p+p-1.f;

float t=(1.f-p)*1.386249f;
float t2=12.f+t*t;
r = res*(t2+6.f*t)/(t2-6.f*t);
};

float MoogFilter::process(float input)
{
// process input
x = input - r*y4;

//Four cascaded onepole filters (bilinear transform)
y1= x*p +  oldx*p - k*y1;
y2=y1*p + oldy1*p - k*y2;
y3=y2*p + oldy2*p - k*y3;
y4=y3*p + oldy3*p - k*y4;

//Clipper band limited sigmoid
y4-=(y4*y4*y4)/6.f;

oldx = x; oldy1 = y1; oldy2 = y2; oldy3 = y3;
return y4;
}

float MoogFilter::getCutoff()
{ return cutoff; }

void MoogFilter::setCutoff(float c)
{ cutoff=c; calc(); }

float MoogFilter::getRes()
{ return res; }

void MoogFilter::setRes(float r)
{ res=r; calc(); }

I see where the exp() comes from. It just models the resonance. I think it needs more work. At high frequencies it goes into self-oscillation much more quickly than at low frequencies.

A much better tuning seems to be
k=2*sin(f*pi/2)-1;

(within a 0.1 cent up to 4kHz, at 44.1kHz sample rate)

This filter works and sounds fine in my VST.
I've re-written the code using templates, which makes life easier when switching between <float> and <double> implementation.



#pragma once

namespace DistoCore
{
  template<class T>
  class MoogFilter
  {
  public:
    MoogFilter();
    ~MoogFilter() {};

    T getSampleRate() const { return sampleRate; }
    void setSampleRate(T fs) { sampleRate = fs; calc(); }
    T getResonance() const { return resonance; }
    void setResonance(T filterRezo) { resonance = filterRezo; calc(); }
    T getCutoff() const { return cutoff; }
    T getCutoffHz() const { return cutoff * sampleRate * 0.5; }
    void setCutoff(T filterCutoff) { cutoff = filterCutoff; calc(); }

    void init();
    void calc();
    T process(T input);
    // filter an input sample using normalized params
    T filter(T input, T cutoff, T resonance);

  protected:
    // cutoff and resonance [0 - 1]
    T cutoff;
    T resonance;
    T sampleRate;
    T fs;
    T y1,y2,y3,y4;
    T oldx;
    T oldy1,oldy2,oldy3;
    T x;
    T r;
    T p;
    T k;
  };

    /**
     * Construct Moog-filter.
     */
  template<class T>
  MoogFilter<T>::MoogFilter()
  : sampleRate(T(44100.0))
  , cutoff(T(1.0))
  , resonance(T(0.0))
  {
    init();
  }

    /**
     * Initialize filter buffers.
     */
  template<class T>
  void MoogFilter<T>::init()
  {
    // initialize values
    y1=y2=y3=y4=oldx=oldy1=oldy2=oldy3=T(0.0);
    calc();
  }

    /**
     * Calculate coefficients.
     */
  template<class T>
  void MoogFilter<T>::calc()
  {
    // TODO: replace with your constant
    const double kPi = 3.1415926535897931;

    // empirical tuning
    p = cutoff * (T(1.8) - T(0.8) * cutoff);
    // k = p + p - T(1.0);
    // A much better tuning seems to be:
    k = T(2.0) * sin(cutoff * kPi * T(0.5)) - T(1.0);

    T t1 = (T(1.0) - p) * T(1.386249);
    T t2 = T(12.0) + t1 * t1;
    r = resonance * (t2 + T(6.0) * t1) / (t2 - T(6.0) * t1);
  };

    /**
     * Process single sample.
     */
  template<class T>
  T MoogFilter<T>::process(T input)
  {
    // process input
    x = input - r * y4;

    // four cascaded one-pole filters (bilinear transform)
    y1 =  x * p + oldx  * p - k * y1;
    y2 = y1 * p + oldy1 * p - k * y2;
    y3 = y2 * p + oldy2 * p - k * y3;
    y4 = y3 * p + oldy3 * p - k * y4;

    // clipper band limited sigmoid
    y4 -= (y4 * y4 * y4) / T(6.0);

    oldx = x; oldy1 = y1; oldy2 = y2; oldy3 = y3;

    return y4;
  }

    /**
     * Filter single sample using specified params.
     */
  template<class T>
  T MoogFilter<T>::filter(T input, T filterCutoff, T filterRezo)
  {
    // set params first
    cutoff = filterCutoff;
    resonance = filterRezo;
    calc();

    return process(input);
  }
}

Why samplerate is missing in calc function?

This code works great. I already had a filter in my program so sticking this in only took about an hour. The sound is just what I hoped it would be. I started putting some really gnarly low frequency  square waves through it and it returns that super chewy sound you can get from a Moog. Thanks for this.

This filter works just fine and sweeps just fine almost all the way down, cutoff easily goes below 40 Hz without issue.  I implemented it in Numerical Python (Jupyter notebook) just to be able to see it working and fiddle with it (renders sound to .wav in non realtime of course).

Cutoff sweep sounds good enough, a bit on the clean side compared to the analog Moog filters I've heard.  It starts to ring around res=0.7 and self oscillates fine for almost any res above 1.0.   I find this filter's ringing sounds a bit tinny, thin and rather irritating though.  This seems to be a common problem in DSP filters.  It needs something, a je ne sais quoi of some kind.

Any suggestions how to modify it?