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************************************************************************
FAUST library file
Copyright (C) 2003-2011 GRAME, Centre National de Creation Musicale
---------------------------------------------------------------------
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as
published by the Free Software Foundation; either version 2.1 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA.
************************************************************************
************************************************************************/
declare name "MaxMSP compatibility Library";
declare author "GRAME";
declare copyright "GRAME";
declare version "1.1";
declare license "LGPL";
ba = library("basic.lib");
ma = library("math.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 envelope
//
// 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, ba.if (nt <= 0, value, c+(value - c) / nt)
with {
nt = ba.if( value != value', samples, t-1);
samples = time*ma.SR/1000.0;
};
};
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