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More specifically, I'm curious how we can represent sound waves in a way that would both distinguish between individual voices and also recognize, e.g. that recordings of different people saying the same word contain the same word. That is, if I say "tree", for instance, it would sound different than if you said it, but native English speakers would still recognize it as the same word.
What properties of sound make this possible?

That is, how can two sound waves, such as those created by two different people saying the the word "tree", encode both the information of the word and also the information of each person's "vocal fingerprint", as I've heard it called? What specifically makes the sound of "tree" sound both the same and different when it's said by two different people and how is modeled/quantified mathematically?

Also, to clarify, I'm familiar with the Fourier transform (it's come up in several of my courses involving circuits and digital signals and then in quantum mechanics) and expect that it would be involved in the sort of model I'm asking about, but I'm looking for more specifics.

Also, if this isn't the right site for this question, please let me know what would be a better one. I thought about posting it on the math SE, but figured it was more of a physics question since I'm asking about properties of sound waves.

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    $\begingroup$ What you are asking is a topic of ongoing research and extremely complicated. It is approached in a kind of multidisciplinary way just because of its complexity. It involves the characterisation of (not only) sound waves in a manner that makes sense from a physics perspective (acoustics), the subjective perception of sound (the subject of psychoacoustics) as well as higher cognition functions of the brain (neuro otology). To my understanding (of various levels in each field) there's no specific modelling of sound waves for the purpose of solving this problem but mostly the (cont.) $\endgroup$
    – ZaellixA
    May 28, 2023 at 23:37
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    $\begingroup$ (cont. ed) characterisation of the various transduction mechanisms (from one system to the other, sound $\rightarrow$ psychoacoustics $\rightarrow$ cognition) and the function of each in the broader picture of the problem. $\endgroup$
    – ZaellixA
    May 28, 2023 at 23:39
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    $\begingroup$ Furthermore, you may, or may not have better luck at Signal Processing SE just because the signal processing and condition of the signals involved is just part of the whole picture. You could try asking there but most probably you will get answers related to the topics of Speech Processing and Natural Language Processing. I am not sure this is what you are asking for but if it is closer to what you seek then you should ask there. $\endgroup$
    – ZaellixA
    May 28, 2023 at 23:42
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    $\begingroup$ @Ghoster, "ear" encompasses the first stages of that signal processing in a way that "microphone" does not. A microphone is just a transducer. An ear is more than that. $\endgroup$ May 29, 2023 at 1:02
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    $\begingroup$ Physics ends where acoustic energy is converted in electrical or chemical energy. This is definitely not a physics question. $\endgroup$
    – FlatterMann
    May 29, 2023 at 1:35

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I think, for speech synthesis, they have modeled different accents for English (or some given language). I am not sufficiently familiar with this to know what accents and what languages they have modeled.

I presume, for speech recognition, there is some pitch tracking on syllables that might be consistent with the synthesis of words of a given accent of a specific language. Also in the speed of enunciation, which can maybe be measured, if a word is recognized.

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