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Does anybody have a good definition for "noise" that includes all aspects of it?

I vaguely remembered something like :

"noise is a signal that does not contain any relevant information to the animal/individual/process of interest"

but I must have gotten something wrong because a signal is defined by the fact it carries information... Any thoughts/references to rephrase my sentence?

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Seems like a bit of a textbook question, so here's the answer from the textbook on my shelf, Lurton (2010):

Noise is an important issue in underwater acoustics, covering many different physical processess. [...] The causes of noise can be grouped into four categories: ambient noise, self-noise, reverberation, and acoustic interference.

From these definitions it can be seen that "noise" is a concept more related to its role and consequences than to a specific acoustic content. Structurally, noise can indeed correspond to very different waveforms: either random in the case of ambient noise or diffuse echoes from the transmitted signal in the case of reverberation, or even clearly recognizable and stable signals for interference caused by other instruments.

Though the definition is from a text on underwater acoustics, the definition of noise appears to me to be medium agnostic.

Reference:

Lurton, X (2010) An Introduction to Underwater Acoustics: Principles and Applications. Chapter 4 Noise and signal fluctuations. Springer-Verlag Berlin.

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  • $\begingroup$ I Think this is a very useful comment. I also always appreciated Chris Clark's general definitions: Target: your signal of interest; Clutter: signals from conspecifics that may have other biological relevance, but just not to your study; Noise: all other signals interfering with your target (ambient, anthropological, etc.). $\endgroup$ Nov 20, 2023 at 10:22
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Apart from the old observation : "one man's noise is another man's signal" (see also https://english.stackexchange.com/questions/89577/origin-of-one-mans-noise-is-another-mans-signal ) the meaning/quality/definition is discussed for long time, sometimes also controversly, indicating that definition depends heavily on the context.

Your quote reflects on this in the final part, the only weird part is the term 'signal', but is one replaces 'signal' by 'data' similar to

"noise is data that does not contain any relevant information to the animal/individual/process of interest"

then it could make sense is all scanarios including

  • signal detection: data are divided in signal and noise
  • noise polution: sound (acoustic data) that does not belong to the environment is described as noise
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Daniel Fink wrote a nice short paper on this issue in 2019: "A new definition of noise: noise is unwanted and/or harmful sound. Noise is the new ‘secondhand smoke’" https://doi.org/10.1121/2.0001186.

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  • $\begingroup$ Not sure if I would call this a "nice" paper. It is good enought, though, for generating a discussion. Also,IMO, too much focused on possible harming effects of noise polution. $\endgroup$
    – WMXZ
    Oct 7, 2023 at 7:00
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I think it is more of rephrasing or broadening the definition of signal than the definition of noise, also being dependent on context.

Strict sense of signal

In a more strict sense, when we talk about SNR (signal to noise ratio), for example, then noise is not a signal, because "signal" is then closer to your definition, which is the relevant part of the broader signal.

Broader sense of signal

This "broader signal", from which noise is a part of, is what's been captured by a sensor, a measurement system, or is some general data transformed in some way to what we would call a signal (a numeric array of data that relates to one or more independent variables). However, if you're using a microphone to capture vibrations in air, even if it's "noisy" (e.g. it's random fluctuations), it's still what you're trying to capture from the environment in general (you're not getting temperature information, surface rugosity, light, etc.), so it would still be relevant for your purposes in a sense.

Supporting with a reference

I think the SNR part is already clear and more intuitive, but Oppenheim and Willsky's book may help to clarify what I mean in the third paragraph. Translating from a portuguese edition of Signals & Systems:

"The signals, which are functions of one or more independent variables, contain information about the behaviour or nature of some phenomenon, while systems answer to particular signals, producing other signals or some desired behaviour."

So if all you're measuring from a microphone is noise, the information it's carrying is that the sound behaviour (at that time and place) is noisy - and then this "noise" would still be a signal.

Complement

Checking the Wikipedia page on signal, in the first paragraph, we notice that the "it conveys information" role is not emphasized by all authors. In the audio signal Wiki, it is simply "a representation of sound".

Reference

Alan V. Oppenheim, Alan S. Willsky. Sinais e sistemas, 2 ed. Pearson. 2010. ISBN 978-85-4301-380-0.

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