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Hilbert transform code

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DrDoug

Joined: Feb 14, 2011
Posts: 3
Location: Cambridge

Posted: Sun Apr 01, 2018 5:47 am Post subject: Hilbert transform code

In case it's useful to anyone, here's the "Hilbert transform" ported from Pure Data.

Code:

///////////////////////////////////////////////////
// hilbert.ck - v1.0 - Douglas Nunn, April 2018
//
// IIR "Hilbert transform" - porting [hilbert~] from Pure Data to ChucK
// ("the name is abused here according to computer music tradition")
// (I Can't Believe It's Not The Analytic Signal)
//
// This is a pair of 4th-order all-pass filters whose outputs somehow manage to be about
// 90 degrees out of phase from each other. Both have different phases from the original.
// Adapted from a 4X patch by Emmanuel Favreau, circa 1982.
//
// Note that the signs of a1 and a2 are flipped compared to the pd parameters.
// This is because ChucK's BiQuad is implemented differently to pd's [biquad~].
// References
// https://ccrma.stanford.edu/~jos/filters/Direct_Form_II.html
// https://en.wikipedia.org/wiki/Digital_biquad_filter#Direct_form_2
// https://github.com/olilarkin/OL-OWLPatches/blob/master/IIRHilbert.dsp - FAUST code

class HilbertOne extends Chubgraph
{
inlet => BiQuad out1filter1 => BiQuad out1filter2 => outlet;
// [biquad~ -0.02569 0.260502 -0.260502 0.02569 1]
0.02569 => out1filter1.a1;
-0.260502 => out1filter1.a2;
-0.260502 => out1filter1.b0;
0.02569 => out1filter1.b1;
1.0 => out1filter1.b2;
// [biquad~ 1.8685 -0.870686 0.870686 -1.8685 1]
-1.8685 => out1filter2.a1;
0.870686 => out1filter2.a2;
0.870686 => out1filter2.b0;
-1.8685 => out1filter2.b1;
1.0 => out1filter2.b2;
}

class HilbertTwo extends Chubgraph
{
inlet => BiQuad out2filter1 => BiQuad out2filter2 => outlet;
// [biquad~ 1.94632 -0.94657 0.94657 -1.94632 1]
-1.94632 => out2filter1.a1;
0.94657 => out2filter1.a2;
0.94657 => out2filter1.b0;
-1.94632 => out2filter1.b1;
1.0 => out2filter1.b2;
// [biquad~ 0.83774 -0.06338 0.06338 -0.83774 1]
-0.83774 => out2filter2.a1;
0.06338 => out2filter2.a2;
0.06338 => out2filter2.b0;
-0.83774 => out2filter2.b1;
1.0 => out2filter2.b2;
}

// testing
SinOsc ef;
Std.mtof(63) => ef.freq;
0.5 => ef.gain;

ef => HilbertOne h1 => dac.chan(0);
ef => HilbertTwo h2 => dac.chan(1);

dac => WvOut2 w => blackhole;
me.dir()+"testhilbert.wav" => w.wavFilename;
null @=> w;

1982::ms => now;
/**/

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