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I have two devices that generate different classes of signals, one simple and one complex. I would like to find a single word or short phrase that describes the increased richness in one class compared to the other. I'm wondering if such a word or phrase exists.

Class #1 is limited to pure tones and colored noise. These sounds are time-invariant, and they are described as having attributes of "frequency and duration," where frequency is taken to mean any number of frequencies together, so long as they are invariant over time.

Class #2 may be any kind of sound. Typically the sounds used are more complex than those in class #1, with time-varying features. They usually have phase and amplitude changes affecting various frequencies over time. Often they contain semantic content such as recognizable real-world sounds or spoken words. This class of sound has been loosely described as having an attribute of "spectral content" as opposed to an attributes of "frequency and duration," but that description doesn't seem to be very good because people may consider spectral content to mean a distribution of time-invariant frequencies.

Perhaps "time-varying spectral content" gets closer? That might be a problem, because the rich class is a superset of the simple class, so there's no requirement for a signal to vary over time. In any event, I'm not sure having time-varying spectral content rather than a frequency and duration really captures the qualitative difference between white noise and a song fragment. Spectro-temporal variations seem to be part of it, and the temporal envelope is certainly important .

Rich sounds would be things like a child laughing, a dog barking, or a human speaking your name, while simple sounds would be things like an 800 Hz sine wave, or white or pink noise.

Is there a pre-existing word or short phrase that meaningfully describes the kind of sonic richness that distinguishes one from the other?

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    $\begingroup$ If it is Random the correct term would be Non Stationary. $\endgroup$ – Royi Jun 4 at 6:23
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    $\begingroup$ I don’t think there is a standard word. perhaps “natural sounds” would suffice $\endgroup$ – Stanley Pawlukiewicz Jun 4 at 14:44
  • $\begingroup$ @Royi I don't think "Non Stationary" would distinguish rich sounds from simple sounds, because a short burst of white noise or pure tone would also be non stationary, right? $\endgroup$ – Craig.Feied Jun 4 at 16:08
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    $\begingroup$ In addition to Royi's comment, In electrical-engineering (esp. communications) the class of test signals that have (deterministically) time-varying spectrum are termed as chirp in general. There are linear and nonlinear variants etc.. $\endgroup$ – Fat32 Jun 5 at 11:26
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    $\begingroup$ I would call the Class #1 signals "stationary" or "quasi-stationary". I would call most in the Class #2 "nonstationary", If there is any periodicity noticeable in the sound, I would call this property "quasi-periodic", although I realize the math guy have a different meaning to that term. $\endgroup$ – robert bristow-johnson Jul 6 at 23:34
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The notions of harmonicity or non-stationary seem connoted.

Stochastic White noise or pink noise, or deterministic pure tones, are (strongly) structured in the spectral domain. So, strongly structured, or strongly spectrally-structured. So, in a soft manner, I would describe the rich class as weakly structured, or weakly spectrally-structured.

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Sounds with predictable frequencies over time periods are of low complexity, highly complex sounds are said to be stochastic ie random or have a high kolmogerov complexity or high entropy.

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If you have two distinct classes, which people are familiar with, the labels you use in your first sentence should suffice, with a twist: Simple or complicated. You want to avoid the word "complex" in this context as it has a definite signal processing meaning already. The other single word variant I can think of from your description would be "steady" or "varying".

This is an old bumped post. Out of curiosity, what did you decide?

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  • $\begingroup$ I was revising claims on a patent where the written description gave examples but did not define any term for the general case. The original written description cannot be amended to add new information. You can be your own lexicographer in a patent application, but only when writing the original application -- not when amending claims -- so I needed to find a term of art that would be universally understood by a person having ordinary skill in the art, and would be completely unambiguous. I went with nonstationary vs stationary or quasi-stationary as per one of the comments. $\endgroup$ – Craig.Feied Aug 7 at 18:02

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