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After looking for something like this, I have found only IPA as a system that tries to represent human sounds with symbols; but there is an argument that IPA does not actually represents the sounds themselves, but instead it defines them in terms of how they are produced by human organs.
So I wonder: do we really have a standard phonetic alphabet that maps to the actual sounds that humans can produce and distinguish?
There seem to be two questions here, one about alphabet and the other about acoustics. The IPA as standardly conceived is an alphabet (it reduces continuous speech to segments), but the letters are defined in terms of articulatory and aerodynamic properties. You could in principle make the IPA into an acoustic alphabet by replacing the production-oriented definitions with acoustic ones. Right now it is possible to translate IPA letters into phonological features (SPE style), and there is more or less a stranslation from SPE articulatory features to the acoustic features of Jakobson, Fant and Halle, except for some reasonably well-understood differences (features like "mellow", "grave").
However, when you talk about "the actual sound human could produce and distinguish", we do not know what that is. For example, it is well-known that the quality of the vowel [i] as written in IPA actually varies across languages quite a lot. IPA does not purport to represent all of the sounds that people can produce and distinguish (even limiting sounds to language sounds). Instead, it purports to represent all of the sounds which can be "phonemic" in human languages.
There are a bunch of diacritics that can be used to fine-tune the "exact" sound as used in a real language, but there is no unambiguous way to denote the "k" of Kabardian as distinct from the "k" of various languages.
I might mention another way to derive acoustic definitions of IPA letters (a "do it" research project, not a "look it up" project). There are a number of expert recordings of IPA letters, vowels in a steady state and consonants in the environment pair "Ca aˈCa". These could be studied acoustically, for example to get the average formant trajectory of utterances exemplifying each letter. This is essentially researchifying the old-style way of learning IPA, where students would mimic the pronunciations of the instructor, who had (some degree of) expertise in the IPA. Samples from Ladefoged, Esling, House and Wells are available, and there may be other sources (there are Jones cardinal vowel recordings; and I just discovered that the Smalley recordings are on the web but they should be vetted for IPA-correctness – they don't have a consistent vowel in the CV context).
Right now it is possible to translate IPA letters into phonological features (SPE style) This is what I also wish that it should be defined as standard like IPA somewhere but cannot found it
Short answer: no, no such thing exists.
Alternately: does a spectrogram qualify?
Long answer: there are quite a few problems with precise acoustic transcription.
In particular, spoken sound isn't divided into nice distinct units. When an English-speaker says [khæt], the actual acoustic reality is silence, then a tiny bit of turbulence, then a continuous vowel sound, then silence again. The [k] and the [t] don't have any acoustic existence in and of themselves—the only sign of them is how the [æ] gets warped at the beginning and end.
How would an "acoustic phonetic alphabet" deal with this in a useful way? If you record someone saying [æk] versus [æp], or [uk] versus [up], you'll see a different "warping" effect in all four of those, with none of them "warping" in quite the same way. But a human listener will process and interpret all those effects subconsciously without needing to think about it, and tell you that [æk] and [uk] have the same consonant, and [æp] and [up] have the same consonant, and those two consonants aren't the same.
And articulatory studies show that, indeed, there is something the same between [æk] and [uk], and between [æp] and [up], and that something is where the closure occurs in the vocal tract—the place where the airflow is cut off. So that's what the IPA represents, not an acoustic fact, but an articulatory one. Not because it's more accurate or anything like that, but because in this case, the articulatory facts are more useful for linguists than the acoustic ones. When precise acoustic details are needed, phoneticians tend to stick to spectrograms, which can represent all those details more completely and precisely than any alphabet could.
[kæ] and [ku] have a lot less in common, acoustically, than one would expect. The main similarities are in the articulation, not in the acoustics. This is why I don't know of any speech recognition or TTS system that works with individual phonemes. The smallest unit commonly used is the diphone.
