//SLUGens released under the GNU GPL as extensions for SuperCollider 3, by Nick Collins, http://composerprogrammer.com/index.html

NL2 Arbitrary Non Linear Filter Equation

NL.ar(input, bufnuma, bufnumb, guard1, guard2, mul, add)

Represents the arbitrary non-linear filter difference equation in the time domain:

y(n) = sum over terms of      constant * product of x terms at individual powers * product of y terms at individual powers

This allows arbitrary crossterms in x and y, but is expensive to calculate. 

Stability is definitely not guaranteed; most equations will quickly blow-up. See the guard arguments below. It is recommended that you stick to positive exponents for signals which are within -1 to 1, else explosion of values is inevitable. 

(0.1)**(-1.26)  //negative exponents cause blowup for smaller signals abs(sig) < 1.0

(1.1)**(2.26)  //positive exponents cause blowup for larger signals abs(sig) > 1.0

You need to pass in the parameters via two buffers, of arbitrary size.

input- What do you want to filter?

bufnum- A single buffer containing numcrossterms in the first index, then the specification of crossterms as (constant, num x terms, list of x index/exponent pairs, num y terms, list of y index/coefficient pairs). Buffer contents can be switched at run-time as longas this data format is strictly adherred to. 

maxasize- Maximum index stored for previous outputs

maxbsize- Maximum index stored for previous inputs

guard1-  Watch out for blow-up and reset if necessary; this is the value of the maximum absolute output allowed. 

guard2-  Watch out for blow-up and reset if necessary; this is the value of the maximum absolute change of output allowed. 

 On discovering blow-up, filter output is set back to zero for all stored outputs, so that feedback cannot occur.  

(

a=[2,   0.5, 1, 0, 1,  0,   -0.35, 0, 2, 5, 2, 3, 0.5]; //specification of crossterms

c=Buffer.sendCollection(s, a, 1);

)

{SinOsc.ar(MouseX.kr(440,1760),0,0.2)}.play //without

//subtle distortion

{NL2.ar(SinOsc.ar(MouseX.kr(440,1760),0,0.5),c,1, 6).clip2(1.0)}.play //with

//random buffers

(

a=[10]++(Array.fill(10,{var bsize, asize; bsize= rrand(1,3); asize=rrand(0,3); 

[0.5.rand2,bsize]++(Array.fill(bsize,{[rrand(0,20), exprand(0.1,6)]}).flatten) ++ [asize] ++ (Array.fill(asize,{[rrand(0,20), exprand(0.1,6)]}).flatten);

}).flatten);

 //feedback coefficients

c=Buffer.sendCollection(s, a, 1);

)

{NL2.ar(AudioIn.ar(1),c,21,21).clip2(1.0)}.play //with

//WARNING; CAN BE VERY CPU EXPENSIVE AND NOISY!

(

//limited update

r= {

inf.do{

var e; 

var num; 

num=rrand(2,10);

e=[num]++(Array.fill(num,{var bsize, asize; bsize= rrand(1,3); asize=rrand(0,3); 

[0.5.rand2,bsize]++(Array.fill(bsize,{[rrand(0,20), exprand(0.1,6)]}).flatten) ++ [asize] ++ (Array.fill(asize,{[rrand(0,20), exprand(0.1,6)]}).flatten);

}).flatten);

if(e.size<=a.size,{

c.sendCollection(e);

});

1.0.wait;

}

}.fork; 

)

r.stop;

//larger sparse arrays; some may lead to silence

(

a=[10]++(Array.fill(10,{var bsize, asize; bsize= rrand(1,2); asize=rrand(0,1); 

[0.7.rand2,bsize]++(Array.fill(bsize,{[rrand(0,999), exprand(0.1,6)]}).flatten) ++ [asize] ++ (Array.fill(asize,{[rrand(0,999), exprand(0.1,6)]}).flatten);

}).flatten);

 //feedback coefficients

c=Buffer.sendCollection(s, a, 1);

)

{NL2.ar(AudioIn.ar(1),c,1000,1000).clip2(1.0)}.play //with

(

var e; 

var num; 

num=rrand(2,10);

e=[num]++(Array.fill(num,{var bsize, asize; bsize= rrand(1,2); asize=rrand(0,1); 

[0.7.rand2,bsize]++(Array.fill(bsize,{[rrand(0,999), exprand(0.1,6)]}).flatten) ++ [asize] ++ (Array.fill(asize,{[rrand(0,999), exprand(0.1,6)]}).flatten);

}).flatten);

if(e.size<=a.size,{

c.sendCollection(e);

});

)