> Если сигнал представить в виде s(t)=S(t)*cos[Ф(t)], тогда величина dФ(t)/dt есть та самая мгновенная частота.

«Формула»—то «мгновенной частоты» оттуда, да? И где она там? В котором из трех?

Третий «учебник», судя по ссылке, это статья. В умном журнале. p. III, должно быть, стр. 111.

Не мое дело, говорите? Ну, не мое, так не мое. Продолжайте, пожалуйста. Попкорном я запасся, спасибо.

Еще советую Вам в science_freaks@lj о Ваших изысканиях в теории сигналов написать. Там любят, когда сами приходят.

Формула во всех трех есть. Что касается статьи, то p. III - это типа третий том, страница тоже нужна, да? А то ведь могу посмотреть.

Вообще, если с термином "мгновенная частота" не знакомы, то это не значит, что я его сам придумал.

He is correct. Just think of a chirped signal. This terminology may sound unusual only because it is more common in optics and acoustics to look at the individual harmonics and interpret the phase as a function of frequency, splitting it into group velocity dispersion and higher dispersion terms. The "instant frequency" is a complementary, time domain look at the same phase. We use it in short-pulse laser optics all the time. Here is an introductory text
http://books.google.com/books?id=Ro2bAyZ1bH4C&pg=PA472&lpg=PA472&dq=%22instant+frequency%22+light&source=web&ots=b49LSq3Ngq&sig=VyXEAbpkx-m7__MIo7352AhbQPY

Your conceit is unwarranted.

> He is correct.

Before even trying to argue, let me restate your position to prevent us from falling into a traphole of a blanket statement. Your statement covers one or more of his assertions, namely that:
a) the instantaneous frequency (IF) can be sensibly defined;
b) and its definition for the signal s(t)=S(t)*cos[Ф(t)] is dФ(t)/dt;
c) and this definition is in all three mentioned books, which are indeed books (this may be quite a minor issue except that it was used as an argument against my point, and therefore should be answered);
d) that the brain “reacts” (whatever that means, it cries for clarification) to the IF (only?) of a signal (we are talking acoustics, correct?)
e) the perceived frequency of two simultaneous sines of same amplitude equals their arithmetic mean frequency (IF or spectral frequency? they are same for sine waves, so the question likely does not apply);
f) and that (e) necessarily follows from (d).

Are vindicating Mr. ptrvc on all claims that he's made, or on specific ones only?

My point is that (a) is correct (and, if you want, I was wrong stating otherwise). I also claim that statements (d) through (f) are neither correct nor wrong, but rather freakish. The (b) might be correct, should you omit three characters, although, given the idiocy of other claims (sorry Mr. ptrvc, I just said that), no benefit of doubt is furthered here. As for (c), I believe has been thrown into my face out of bad attitude, and probably irrelevant.

> Your conceit is unwarranted.

Please do not even get me started on that. My deep—religious, if you want,‐belief is that the truth exists, and that relativism is wrong. Therefore, every opinion of everyone may not be discussed on an equal ground. I am adding that just for the record why my manners are deliberately unsubtle; I will not discuss that, if you please. My “conceit” is not relevant to the topic in question.

(b) is the correct definition which is also standard, eg http://cas.ensmp.fr/~chaplais/wavetour_presentation/Intro/Instantanous_Frequency.html
(c) is irrelevant
(d) he is talking about psychophysics of audial perception of, specifically, pitch. How it is perceived is unknown. Perhaps you think that our hearing is based on harmonic analysis. It is not. The two leading theories (there are 200+ of such theories) is pattern recognition and autocorrelation/temporal recognition. Here is a nice review
http://recherche.ircam.fr/equipes/pcm/cheveign/pss/2004_ICA.pdf
It is hard to explain how ear distinguishes tones at the observed sampling rates w/o using some version of temporal perception (see the review) as it circumvents Helmholtz limit. The basic idea is that the vibrations are clocked vs firing electrical pulses by groups of synchronized cochlean neurons (to synthesize a kHz wave through a superposition of groups of 100 Hz pulses). It takes only 2 cycles for a sine way, and in this sense temporal perception is instantenous; so are some versions of autocorrelation, with suitable filtering. It is not exactly the IF that is measured, but it is not exacly the power spectrum that can be measured by the "harmonic analyser" or the "autocorrelator". There is always a compromise between frequency resolution and the speed of processing.
(e) this may or may not be true according to one's theory of audial perception, but none of the modern theories claim that the ear works as a harmonic analyzer resolving partials into Fourier components. For starters, you will perceive pitch even without the fundamentals. Even without those, imagine that the two frequencies are so close that sampling (w1-w2)/2 takes many cycles of (w1+w2)/2. The reverberation will confuse temporal perception into believing there is a single pitch and his statement will be correct. He, though, says that it is always correct, I do not understand why and so I've asked him why. He strikes me as a person knowing what he is talking about, but not too good at communication.

I do suggest you reading this review to check your intuition, if nothing else; it is also an interesting open problem. It will persuade you how counterintuitive is hearing, how stubbornly it defies the simplistic theories of this process, and how little is known about it with certainty. In such a situation, chastizing others for ignorance looks plain odd. Truth does exist, but you know of it as much as the experts, which in this case freely admit that they are clueless. On this ground, we are all equal. Your manners is your business, but fair is fair.

Ну. Так я, типа, с этого и начал. Мораль истории какая: просветли бамбуковой палкой по башке того, кто с уверенностью скажет, как ухи слышат. Ну я, типа, и того…

Вы хорошо по-русски понимаете? Если непонятно, я переведу, пожалуйста. Боюсь, мы начинаем злоупотреблять импортной речью.

I understand you allright, I just have trouble writing in Russian. So can you explain why it is always true. I thought about it, and I see that in principle that is possible if the combination of temporal pitch recognition and beat amplitude analysis are combined to produce pitch perception. That's probably possible, but WHY? It would be the strangest way of doing it... not that it is impossible, of course. Probably it would be simpler if you'd point us to the specific pitch perception theory you reason from. I think I can figure it out on my own, and if I fail, I can always ask you!

Теория слуха? Отнюдь нет: это, скорее, этическая теория, речь не о слухе. Весь разговор о чем происходит? Некто (а) ученым тоном, ничесоже сумняшеся, (б) путаясь в формулах и терминах, (в) излагает бред (г) когда собеседнику не известна половина ответа. Хрестоматийное сочетание (а)—(г) требует от меня потыкать этого некто мордой в грязь: сочетание это, по моему собственному необъективному критерию, исключает добросовестное заблуждение. Дело не в том, что это было бы мне приятно или хотелось, или мне время больше убить было нечем, а в том, что мне совестно этого не сделать.

И, честно говоря, обсуждение это мне бы хотелось завершить как можно скорее.