Does the Amplitude of White Noise Double When Two Samples are Added Together?

Click For Summary

Discussion Overview

The discussion centers around the behavior of white and pink noise when two samples of equal amplitude are added together. Participants explore the implications of this addition on the amplitude and characteristics of the resulting noise, considering both theoretical and mathematical perspectives.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether adding two samples of white noise results in a single sample with twice the amplitude.
  • Another participant explains that the Fourier transform of the combined samples maintains the white noise characteristic, suggesting that the addition does not simply double the amplitude.
  • A participant seeks clarification on the terminology used in the Fourier transform explanation, specifically regarding constants and the Fourier spectrum.
  • Clarifications are provided about the constants in the Fourier transformation of white and pink noise, as well as the notation used for the Fourier transformations of the individual noise functions.
  • One participant proposes that if the noise sources are uncorrelated, the squared amplitudes should add rather than the amplitudes themselves, implying that average powers sum instead.

Areas of Agreement / Disagreement

Participants express differing views on whether the amplitudes or the squared amplitudes should be considered when adding the noise samples. The discussion remains unresolved, with multiple competing perspectives presented.

Contextual Notes

There are unresolved questions regarding the definitions and implications of the Fourier transforms as they relate to the characteristics of white and pink noise. The discussion also highlights potential misunderstandings in mathematical terminology.

Who May Find This Useful

This discussion may be of interest to those studying signal processing, acoustics, or noise characteristics in physics and engineering contexts.

entropy1
Messages
1,232
Reaction score
72
Suppose you have two samples of white noise of equal amplitude. If you add them together ((sub)sample-by-(sub)sample that is), do you get one sample of white noise with twice the amplitude?

How about pink noise?
 
Physics news on Phys.org
Both white and pink noise are defined by their Fourier transform (see http://applet-magic.com/spectrum1.htm), which is linear.

Suppose you have two time functions of white noise, f(t) and g(t). The Fourier transform of αf(t)+βg(t) is αFf+βFg = αcf+βcg, which is the Fourier transform of another white noise. So αf(t)+βg(t) is white noise.

Likewise, if f(t) and g(t) are pink noise, the Fourier transform of αf(t)+βg(t) is αFf+βFg = αcf/ω+βcg/ω = (αcf+βcg)/ω, which is the Fourier transform of another pink noise. So αf(t)+βg(t) is pink noise.
 
Last edited:
What does cf (and cg) mean? Is it a constant function? Is Ff (Fg) the Fourier spectrum?

My terminology may be faulty; I have enjoyed a scientific education, but I have never been particularly good at math...o_O
 
Sorry, I should have been more careful. If you look in the link I posted you will see that there are constants, c, in the Fourier transformation of white and pink noise. cf and cg are the constants associated with f and g. Ff and Fg are the Fourier transformations of f and g. (I could not get the LaTex script F to work immediately.)
 
If the noise sources are uncorrelated, they shouldn't have any fixed phase relation. I would expect the squared amplitudes to add, not the amplitudes.
 
  • Like
Likes   Reactions: FactChecker
mfb said:
If the noise sources are uncorrelated, they shouldn't have any fixed phase relation. I would expect the squared amplitudes to add, not the amplitudes.
This is not a subject that I am expert at, but I think that means that the average powers sum.
 

Similar threads

Graduate Kalman, White Noise, Sensor Specification, Discretization?
  • · Replies 2 ·
Replies
2
Views
6K
Modern Digital Audio: Understanding Dither and Oversampling in Hi-Res Age
  • · Replies 17 ·
Replies
17
Views
6K
Graduate What does an infinite sum of uniform random variables yield?
  • · Replies 3 ·
Replies
3
Views
9K
Graduate Low value standard deviation bias
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Estimating Gene Mutation Proportion: A & B Approaches
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Power spectral density of a laser's frequency noise
  • · Replies 6 ·
Replies
6
Views
3K
High School Standard Deviation as Function of Sample Size
  • · Replies 24 ·
Replies
24
Views
7K
High School Audio frequency of a humidifier
  • · Replies 12 ·
Replies
12
Views
1K
Python Adding noise and solving stochastic ODEs in Python
  • · Replies 11 ·
Replies
11
Views
4K
High School What exactly is an 'exhaustive event'?
  • · Replies 5 ·
Replies
5
Views
2K