maxmsp.lib

/************************************************************************
************************************************************************
FAUST library file
Copyright (C) 2019-2020 GRAME, Centre National de Creation Musicale
---------------------------------------------------------------------
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************************************************************************
************************************************************************/

declare name "MaxMSP compatibility Library";
declare author "GRAME";
declare copyright "GRAME";
declare version "1.1";
declare license "LGPL with exception";

ba = library("basics.lib");
ma = library("maths.lib");

atodb = db2lin;

//-------------------------------------------------------------------------
//
// Implementation of MaxMSP filtercoeff
//
//	from : Cookbook formulae for audio EQ biquad filter coefficients
//        by : Robert Bristow-Johnson  <rbj@audioimagination.com>
//       URL : <http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt>
//
//-------------------------------------------------------------------------

filtercoeff(f0, dBgain, Q) = environment
{
	//----------------------------------------
	// biquad coeffs for various filters
	// usage : filtercoeff(f0, dBgain, Q).LPF
	//----------------------------------------

		LPF = rbjcoef(a0, a1, a2, b0, b1, b2)
  				with {
				    b0 =  (1 - cos(w0))/2;
				    b1 =   1 - cos(w0);
				    b2 =  (1 - cos(w0))/2;
				    a0 =   1 + alpha;
				    a1 =  -2*cos(w0);
				    a2 =   1 - alpha;
 				};

		HPF = rbjcoef(a0, a1, a2, b0, b1, b2)
  				with {
				    b0 =  (1 + cos(w0))/2;
				    b1 = -1 - cos(w0);
				    b2 =  (1 + cos(w0))/2;
				    a0 =   1 + alpha;
				    a1 =  -2*cos(w0);
				    a2 =   1 - alpha;
  				};

		BPF = rbjcoef(a0, a1, a2, b0, b1, b2) // constant 0 dB peak gain
  				with {
				    b0 =   alpha;
				    b1 =   0;
				    b2 =  -alpha;
				    a0 =   1 + alpha;
				    a1 =  -2*cos(w0);
				    a2 =   1 - alpha;
 				};

  	  	notch = rbjcoef(a0, a1, a2, b0, b1, b2)
  				with {
				    b0 =   1;
				    b1 =  -2*cos(w0);
				    b2 =   1;
				    a0 =   1 + alpha;
				    a1 =  -2*cos(w0);
				    a2 =   1 - alpha;
  				};

		APF = rbjcoef(a0, a1, a2, b0, b1, b2)
  				with {
				    b0 =   1 - alpha;
				    b1 =  -2*cos(w0);
				    b2 =   1 + alpha;
				    a0 =   1 + alpha;
				    a1 =  -2*cos(w0);
				    a2 =   1 - alpha;
 				};

  		peakingEQ = rbjcoef(a0, a1, a2, b0, b1, b2)
  				with {
            		b0 =   1 + alpha*A;
            		b1 =  -2*cos(w0);
            		b2 =   1 - alpha*A;
            		a0 =   1 + alpha/A;
            		a1 =  -2*cos(w0);
            		a2 =   1 - alpha/A;
  				};

  		peakNotch = rbjcoef(a0, a1, a2, b0, b1, b2)
  				with {
            		b0 =   1 + alpha*G;
            		b1 =  -2*cos(w0);
            		b2 =   1 - alpha*G;
            		a0 =   1 + alpha/G;
            		a1 =  -2*cos(w0);
            		a2 =   1 - alpha/G;
  				};

   		lowShelf = rbjcoef(a0, a1, a2, b0, b1, b2)
  				with {
             		b0 =    A*((A+1) - (A-1)*cos(w0) + 2*sqrt(A)*alpha);
            		b1 =  2*A*((A-1) - (A+1)*cos(w0));
            		b2 =    A*((A+1) - (A-1)*cos(w0) - 2*sqrt(A)*alpha);
            		a0 =       (A+1) + (A-1)*cos(w0) + 2*sqrt(A)*alpha;
            		a1 =   -2*((A-1) + (A+1)*cos(w0));
            		a2 =       (A+1) + (A-1)*cos(w0) - 2*sqrt(A)*alpha;
  				};

  		highShelf = rbjcoef(a0, a1, a2, b0, b1, b2)
  				with {
				    b0 =    A*((A+1) + (A-1)*cos(w0) + 2*sqrt(A)*alpha);
				    b1 = -2*A*((A-1) + (A+1)*cos(w0));
				    b2 =    A*((A+1) + (A-1)*cos(w0) - 2*sqrt(A)*alpha);
				    a0 =       (A+1) - (A-1)*cos(w0) + 2*sqrt(A)*alpha;
				    a1 =    2*((A-1) - (A+1)*cos(w0));
				    a2 =       (A+1) - (A-1)*cos(w0) - 2*sqrt(A)*alpha;
				};

	// --------------------- implementation ------------------------------

	// convert rbj coeffs to biquad coeffs
	rbjcoef(a0,a1,a2,b0,b1,b2) = (b0/a0, b1/a0, b2/a0, a1/a0, a2/a0);

	// common values
//	alpha 	= sin(w0)/(2*Q);
//	w0 		= 2*ma.PI*f0/Fs;
	alpha 	= sin(w0)/(2*max(0.001,Q));
	w0 		= 2*ma.PI*max(0,f0)/Fs;
	Fs 		= ma.SR;
	A  		= 10^(dBgain/40);     		// (for peaking and shelving EQ filters only)
	G  		= sqrt(max(0.00001, dBgain));   // When gain is a linear values (i.e. not in dB)
};


//-------------------------------------------------------------------------
// Implementation of MaxMSP biquad~
// y[n] = a0 * x[n] + a1 * x[n-1] + a2 * x[n-2] - b1 * y[n-1] - b2 * y[n-2]
//-------------------------------------------------------------------------

biquad(x,a0,a1,a2,b1,b2) =  x : + ~ ((-1)*conv2(b1, b2)) : conv3(a0, a1, a2)
	with {
		conv2(c0,c1,x) = c0*x+c1*x';
		conv3(c0,c1,c2,x) = c0*x+c1*x'+c2*x'';
	};

//-------------------------------------------------------------------------
//
// Filters using filtercoeff and biquad
//
//-------------------------------------------------------------------------

// Low Pass Filter
LPF(x, f0, gain, Q) 		= x , filtercoeff(f0,gain,Q).LPF : biquad;

// High Pass Filter
HPF(x, f0, gain, Q) 		= x , filtercoeff(f0,gain,Q).HPF : biquad;

// Band Pass Filter
BPF(x, f0, gain, Q) 		= x , filtercoeff(f0,gain,Q).BPF : biquad;

// notch Filter
notch(x, f0, gain, Q) 		= x , filtercoeff(f0,gain,Q).notch : biquad;

// All Pass Filter
APF(x, f0, gain, Q) 		= x , filtercoeff(f0,gain,Q).APF : biquad;

// ????
peakingEQ(x, f0, gain, Q) 	= x , filtercoeff(f0,gain,Q).peakingEQ : biquad;

// Max peakNotch is like peakingEQ but with a linear gain
peakNotch(x, f0, gain, Q) 	= x , filtercoeff(f0,gain,Q).peakNotch : biquad;

// ????
lowShelf(x, f0, gain, Q) 	= x , filtercoeff(f0,gain,Q).lowShelf : biquad;

// ????
highShelf(x, f0, gain, Q) 	= x , filtercoeff(f0,gain,Q).highShelf : biquad;


//-------------------------------------------------------------------------
// Implementation of Max/MSP line~. Generate signal ramp or envelop
//
// USAGE : line(value, time)
// 	value : the desired output value
//	time  : the interpolation time to reach this value (in milliseconds)
//
// NOTE : the interpolation process is restarted every time the desired
// output value changes. The interpolation time is sampled only then.
//-------------------------------------------------------------------------

line(value, time) = state~(_,_):!,_
	with {
		state(t, c) = nt,nc 
		with {
			nt = ba.if(value != value', samples, t-1);
			nc = ba.if(nt <= 0, value, c + (value - c)/nt);
			samples = time*ma.SR/1000.0;
		};
	};