class:: LFGauss
summary:: Gaussian function oscillator
categories:: UGens>Generators>Deterministic

description::
A non-band-limited gaussian function oscillator. Output ranges from strong::minval:: to 1.

LFGauss implements the formula:
code::
f(x) = exp(squared(x - iphase) / (-2.0 * squared(width)))
::
where x is to vary in the range -1 to 1 over the period dur. strong::minval:: is the initial value at -1.

classmethods::
method:: ar, kr

argument:: duration
duration of one full cycle ( for strong::freq:: input: strong::dur = 1 / freq:: )
argument:: width
relative width of the bell. Best to keep below 0.25 when used as envelope. (default: 0.1)
argument:: iphase
initial offset (default: 0)
argument:: loop
if loop is > 0, UGen oscillates. Otherwise it calls doneAction after one cycle (default: 1)
argument:: doneAction
doneAction, which is evaluated after cycle completes (2 frees the synth, default: 0).
See link::Reference/UGen-doneActions:: for more detail.


instancemethods::
method::minval

Returns the lowest value for the given parameters, which is code::exp(1.0 / (-2.0 * squared(width)))::

method::range

Scales the output to the given range. This can be convenient when using LFGauss as an envelope (see example below).

code::
{ LFGauss.ar(0.01, 0.6).range }.plot;
{ LFGauss.ar(0.01, 0.6) }.plot; // starts at about 0.25
::

examples::

subsection:: Some plots

code::
s.boot ;

// a 0.1 second grain
{ LFGauss.ar(0.1, 0.12) }.plot(0.1);

// shifting left
{ LFGauss.ar(0.1, 0.12, -1, loop: 0) }.plot(0.1);

// moving further away from the center
{ LFGauss.ar(0.1, 0.12, 2) }.plot(0.2);

// several grains
{ LFGauss.ar(0.065, 0.12, 0, loop: 1) }.plot(0.3);
::

subsection:: Some calculations

assuming iphase = 0:

strong::minval:: for a given width:
code::minval = exp(-1.0 / (2.0 * squared(width)))::

strong::width:: for a given minval:
code::width = sqrt(-1.0 / log(minval))::

strong::width at half maximum (0.5):::
code::(2 * sqrt(2 * log(2)) * width) = ca. 2.355 * width::

code::
// minval for a width of 0.1:
(exp(1 / (-2.0 * squared(0.1)))) // 2e-22

// maximum width for a beginning at -60dB:
// we want the beginning small enough to avoid clicks
sqrt(-1 / ( 2 * log(-60.dbamp))) // 0.269

// minval for width of 0.25
(exp(1 / (-2.0 * squared(0.25)))).ampdb // -70dB

// maximum is always 1:
{ LFGauss.ar(0.1, XLine.kr(1, 0.03, 1), 0, loop: 1) }.plot(1);

// a gauss curve in sclang:
(0..1000).normalize(-1, 1).collect(_.gaussCurve(1, 0, 0.1)).plot;


// rescale the function to the range 0..1
(
{
	var width = XLine.kr(0.04, 1.0, 1);
	var min = (exp(1.0 / (-2.0 * squared(width))));
	var gauss = LFGauss.ar(0.1, width, loop: 1);
	gauss.linlin(min, 1, 0, 1);
}.plot(1)
);

// range does the same implicitly
(
{
	var width = XLine.kr(0.04, 1.0, 1);
	LFGauss.ar(0.1, width, loop: 1).range(0, 1);
}.plot(1)
);
::

subsection:: Sound examples
code::
// modulating duration
{ LFGauss.ar(XLine.kr(0.1, 0.001, 10), 0.03) * 0.2 }.play;

// modulating width, freq 60 Hz
{ LFGauss.ar(1/60, XLine.kr(0.1, 0.001, 10)) * 0.2 }.play;

// modulating both: x position is frequency, y is width factor.
// note the artefacts due to aliasing at high frequencies
{ LFGauss.ar(MouseX.kr(1/8000, 0.1, 1), MouseY.kr(0.001, 0.1, 1)) * 0.1 }.play;

// LFGauss as amplitude modulator
{ LFGauss.ar(MouseX.kr(1, 0.001, 1), 0.1) * SinOsc.ar(1000) * 0.1 }.play;

// modulate iphase
{ LFGauss.ar(0.001, 0.2, [0, MouseX.kr(-1, 1)]).sum * 0.2 }.scope;

// for very small width we are "approaching" a dirac function
{ LFGauss.ar(0.01, SampleDur.ir * MouseX.kr(10, 3000, 1)) * 0.2 }.play;

// dur and width can be modulated at audio rate
(
{ 	var dur = SinOsc.ar(MouseX.kr(2, 1000, 1) * [1, 1.1]).range(0.0006, 0.01);
	var width = SinOsc.ar(0.5 * [1, 1.1]).range(0.01, 0.3);
	LFGauss.ar(dur, width) * 0.2
}.play
);


// several frequencies and widths combined
(
{
	var mod = LFGauss.ar(MouseX.kr(1, 0.07, 1), 1 * (MouseY.kr(1, 3) ** (-1..-6)));
	var carr = SinOsc.ar(200 * (1.3 ** (0..5)));
	(carr * mod).sum * 0.1
}.play;
)

// test spectrum
(
{
	var son = LeakDC.ar(LFGauss.ar(0.005, 0.2));
	BPF.ar(son * 3, MouseX.kr(60, 2000, 1), 0.05)
}.play;
)
::

subsection:: Gabor Grain

note::
The gaussian function doesn't start with 0 – it asymptotically approaches it at code::-inf:: and code::inf::. When using it as an envelope, it has to start at some smaller value, and it has an offset for this value. You can remove this offset by explicitly setting the strong::range::, e.g. to code::0..1:: (this is the default).
::



code::
(
var freq = 1000;
var ncycles = 10;
var width = 0.25;
var dur = ncycles / freq;
{

	var env = LFGauss.ar(dur, width, loop: 0, doneAction: 2).range;
	var son = FSinOsc.ar(freq, 0.5pi, env);
	son
}.plot(dur);
)


(
SynthDef(\gabor, { |out, i_freq = 440, i_sustain = 1, i_pan = 1, i_amp = 0.1, i_width = 0.25 |
	var env = LFGauss.ar(i_sustain, i_width, loop: 0, doneAction: 2).range;
	var son = FSinOsc.ar(i_freq, 0.5pi, env);
	OffsetOut.ar(out, Pan2.ar(son, i_pan, i_amp));

}).add;
)

// modulating various parameters
(
Pdef(\x,
	Pbind(
		\instrument, \gabor,
		\freq, Pbrown(step:0.01).linexp(0, 1, 100, 14000),
		\dur, Pbrown().linexp(0, 1, 0.004, 0.02),
		\legato, Pbrown(1, 3, 0.1, inf),
		\pan, Pwhite() * Pbrown()
	)
).play
)

// modulating width only
(
Pdef(\x,
	Pbind(
		\instrument, \gabor,
		\freq, 1000,
		\dur, 0.01,
		\width, Pseg(Pseq([0.25, 0.002], inf), 10, \exp),
		\legato, 2
	)
).play
)

// compare with sine grain.
(
SynthDef(\gabor, { |out, i_freq = 440, i_sustain = 1, i_pan = 1, i_amp = 0.1, i_width=0.25 |
	var env = EnvGen.ar(Env.sine(i_sustain * i_width), doneAction: 2);
	var son = FSinOsc.ar(i_freq, 0.5pi, env);
	OffsetOut.ar(out, Pan2.ar(son, i_pan, i_amp));

}).add;
)
::
