Noise module: benefits of normal dist?

DerozerDSP · November 22, 2020, 7:30pm

hi,

was looking at the Noise module, and noticed that for white noise is used “random::normal” instead of “random::uniform” distribution.

why this choice? any benefits in terms of audio? or is it faster on computation?

thanks

DerozerDSP · November 26, 2020, 7:53pm

Bump

unlessgames · November 26, 2020, 9:21pm

random::normal is slower as it calls random::uniform twice and also sin, sqrt, log while computing the Box Muller transform, it does this to produce a gaussian white noise if I understand it correctly.

You can check out the difference in audio quality by A / B testing the WHITE and the BLACK outputs of Noise. BLACK uses uniform instead of normal.

github.com

VCVRack/Rack/blob/2db08f15a00f6792bb3a45db31dd13f94966beed/src/random.cpp#L55


}

uint64_t u64() {
	return xoroshiro128plus_next();
}

float uniform() {
	return (xoroshiro128plus_next() >> (64 - 24)) / std::pow(2.f, 24);
}

float normal() {
	// Box-Muller transform
	float radius = std::sqrt(-2.f * std::log(1.f - uniform()));
	float theta = 2.f * M_PI * uniform();
	return radius * std::sin(theta);

	// // Central Limit Theorem
	// const int n = 8;
	// float sum = 0.0;
	// for (int i = 0; i < n; i++) {
	// 	sum += uniform();

Xenakios · November 26, 2020, 9:45pm

Normal/Gaussian noise is what you would expect to get from “natural” sources. Like was mentioned above, there’s also the “black” noise output that produces random numbers from a uniform distribution. I think there isn’t any appreciable differences if you listen to the raw outputs, but you might be able to coax out some differences if you process the noise further. (edit : the Gaussian white noise seems to be a bit more louder than the uniform noise in the Rack Noise module implementation.)

Nowhk · December 1, 2020, 3:24pm

Yes they seems pretty the same.

I don’t really get any differences between the two as well. As @Xenakios point out, they just differs in level.

Tried to process it futher (i.e. not simple raw sound), but still play quite the same…

Follow the post, I’m curious…

unlessgames · December 1, 2020, 3:31pm

Yeah, I meant more like “see if you can find the difference”

Filtering the noise might highlight differences as the distinction between the two supposed to be related to the frequency contents.

You could try with high samplerate as well.

hamptonio · December 1, 2020, 5:31pm

Perhaps the biggest difference is the range; the uniform (black) output will always be -5 to 5, while the normal (white) output could be anything; in practice it isn’t too unusual to see the white range outside of -10 to 10. The excursions are rare enough that they don’t affect the sound directly too much, but it could be important if you are using the sources for control, e.g. in a sample & hold it could make a very big difference.

Squinky · December 2, 2020, 1:03am

as everyone has said - they sound the same. exactly the same. But for non-audio uses they are different.

marc_boule · December 2, 2020, 1:18am

I find it intriguing that they have the exact same spectrum, but look different on a scope, and are mathematically quite different.

Squinky · December 2, 2020, 1:51am

it is cool.