the beginnings of a beautiful era for audio dsp

[xoxos]

i like that part in evil flow,
cos i'm modeling the future over and over
except it's like, the future, and, over like, over

clever things, appeal to the intellect, tricky

or like right there
the horns of the lord above, brother
see the horns on me - i get blowed
before they get to you - i get stuck
come see the horns on a big bad demon

course it's got that horn sound in the background. clever though. "doctor xo"

[xoxos]

adding the saw.

normalisationsynthesis.png

[Architeuthis]

viewtopic.php?p=6656238#p6656238

Code: Select all

double t = s0;
s0 = s0 * w0 + s1 * w1;		//	circular oscillator
s1 = s1 * w0 - t * w1;

x = s0 * *in2;				//	scale
t = s1 + *in4;				//	offset
			
y = t * m0 - x * m1;		//	angle
x = x * m0 + t * m1;

*out1 = y / sqrt(x * x + y * y);

Has anyone been able to translate this into working C++ code? I'm too math-illiterate

oh wait I'm seeing something here.

rotation is defined as:

Code: Select all

*X = x * cos(angle) - y * sin(angle);
*Y = x * sin(angle) + y * cos(angle);

is this correct?

but it looks somewhat different than tis

Code: Select all

s0 = s0 * w0 + s1 * w1;		//	circular oscillator
s1 = s1 * w0 - t * w1;

y = t * m0 - x * m1;		//	angle
x = x * m0 + t * m1;

I'm guessing w0/w1/m0/m1 are -1 to +1 values coming out of a sin/cos function, so

m0 = cos(m);
m1 = sin(m);

w0 = cos(w)
w1 = sin(w)

s0,s1 is internal updated variable
x,y is the output

that leaves t, m, w, in2, in4 variables unknown
in2, in4 are parameters... t, m, w, not sure. one or two of those is phase?
t is angle?

that means m and w. 90 degrees phase different from a single phase/angle value?

[Architeuthis]

I want to possibly turn this into an envelope generator.

here's my attempt at C++ code, I don't know what to do with s0, s1, w0, w1. One of them is definitely phase.

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	double xoxos(double s0, double s1, double angle_m0, double angle_m1, double w0, double w1, double scale, double offset)
	{
		double x, y, t = s0;		

		s0 = s0 * w0 + s1 * w1;
		s1 = s1 * w0 - t * w1;

		x = s0 * scale;
		t = s1 + offset;

		y = t * angle_m0 - x * angle_m1;
		x = x * angle_m0 + t * angle_m1;

		return y / sqrt(x * x + y * y);
	}

[Architeuthis]

here's working version using formula given earlier, but it is not recursive, it just takes in a phase.

Code: Select all

  	double xoxos(double phase, double A, double B_sin, double B_cos, double C)
	{
		double sin_x, cos_x;
		sinCos(phase, &sin_x, &cos_x);

		double sqrt_val = sqrt(pow(A + cos_x, 2) + pow(C*sin_x, 2));
		double out = ((A + cos_x)*B_cos + (C*sin_x)*B_sin) / sqrt_val;

		return out;
	}

[antto]

st0 and st1 are used as state variables
this is a recursive structure, not a mere function

[Architeuthis]

st0 and st1 are used as state variables
this is a recursive structure, not a mere function

ok yes! So please correct my c++ code, i waaant iiiit

removed attempt 1

[Architeuthis]

attempt 2

Code: Select all

class XoxosOscillator
{
public:

	void setFrequency(double v) 
	{ 
		double phaseInc = (v*4)/sampleRate * PI_z_2 + PI_z_2;
		sinCos(phaseInc, &w0, &w1);
	}
	void setSampleRate(double v) { ; }
	void setAngle(double v) { sinCos(v, &m0, &m1); }
	void setScale(double v) { scale = v; }
	void setOffset(double v) { offset = v; }

	double getSample()
	{
		double x, y, t = s0;

		s0 = s0 * w0 + s1 * w1;
		s1 = s1 * w0 - t * w1;

		x = s0 * scale;
		t = s1 + offset;

		y = t * m0 - x * m1;
		x = x * m0 + t * m1;

		return y / sqrt(x * x + y * y);
	}

protected:
	double s0 = 0, s1 = 1;
	double w0 = 0, w1 = 1;
	double m0 = 0, m1 = 1;

	double
		sampleRate = 44100,
		frequency = 1,
		scale = 0,
		offset = 1;		
};

[Architeuthis]

removed attempt 3

[Architeuthis]

ok so attempt 2 is the most correct so far, and im correcting my earlier post for the formula that just takes in phase.

all i need to know is how to convert pi/2 to pi range to frequency.

[Architeuthis]

ok i got frequency control but I have no idea wtf I'm doing,

what is this equation? and I'm not sure it's correct to call the result phaseInc... maybe call it rotationSpeed?

Code: Select all

void setFrequency(double v) 
{ 
	double phaseInc = (v*4)/sampleRate * PI_z_2 + PI_z_2;
	sinCos(phaseInc, &w0, &w1);
}

[Smashed Transistors]

Rotations are good because they preserve signal energy (i.e sum of their squares).

To sort things out, maybe, you can have a look at :

https://ccrma.stanford.edu/courses/250a ... ilters.pdf

It shows how a pass band filter can be implemented with a rotation/scale i.e. a complex multiplication.
This implementation is very stable even with audio rate frequency modulation .


I've derived a simple variant - much simpler than your attempts - of the Matthews filter.
Non linear modulation of the rotation depending on the input or/and output.

Even this basic variation leads to interesting sort of filtering/distortion.

I used this principle in a Reaper synth (cXf synth available in the Reaper Stash) :

https://soundcloud.com/thierry-rochebois-1/test-cxf03
https://soundcloud.com/thierry-rocheboi ... nth-rev-07

It uses a pair of sines as an input to a self-non-linearly-frequency-modulated Matthews filter.

Now... imagine this with coupled units.. and even delays in the feedback loops...
There is so many possibilities to experiment with !

[mystran]

Rotations are good because they preserve signal energy (i.e sum of their squares).

In exact arithmetics, yeah.. in floating point, not so much. Rounding errors with "naive rotation" lead to both phase drift (=wrong frequency) and amplitude drift (which should be fixed periodically).

To get you an idea of how much the accuracy can cause trouble, one of the first version of my FFT used naive rotations. It turns out that (in double precision!) this made an FFT unstable somewhere around 1 million points (maybe earlier, I don't know). There are better recurrences though (eg. the undamped ZDF-SVF is a good one).

[Smashed Transistors]

ZDF-SVF can be cool to experiment with

Is ZDF-SVF stable with audio rate frequency and Q modulations ?

[mystran]

ZDF-SVF can be cool to experiment with

Is ZDF-SVF stable with audio rate frequency and Q modulations ?

Yeah. It essentially comes down to damped rotations, just calculated in a different way.