...simply that there are in fact audible differences... which suggests to me that we don't know everything yet. [1] For example, while there have been plenty of studies done on the range of frequencies audible to humans, they've all been done with continuous steady state sine waves. ([2] Most folks agree that most humans with excellent hearing can hear frequencies between 20 Hz and 20 kHz - although one study extends the bottom of the range to 10 Hz.) [3] However, less direct concepts, like how much phase shift between the left and right it takes to produce an apparent shift in the left/right position of something in the sound stage, are more difficult to measure, And measurements that involve transient and varying waveforms even more so. ([4] Virtually all of the math that describes things like the Nyquist frequency, and the ability to accurately represent waveforms with limited numbers of samples, assumes a continuous sine wave signal.... which music is NOT. [4] Likewise, even the math that describes how a DAC works assumes that the DAC uses something called a "SinC function" when, in reality, the sampling process used by DACs is really only an approximation of it.)
Hopefully without causing too much ill feeling, I have to say that I find some of your posts a little troubling. It's not that they're overtly incorrect, it's that they sometimes appear (IMHO) to expand the grey areas, to suggest implications which are, or very easily could be, misleading. Although it maybe entirely a coincidence, some of your statements appear virtually idetical to those exploited by marketing departments in order to deliberately mislead consumers and then quoted (typically inappropriately) by audiophiles. How many times have we seen these types of responses from audiophiles when challenged over some ludicrous claim: "Science doesn't know everything yet", "we can't measure everything", "music isn't just a sine wave", "digital audio is just an approximation", etc?
1. While strictly true, this statement omits some pertinent facts and the implication is: Maybe if we used music instead of "continuous steady state sine waves" we might discover that the range of audible frequencies extends higher than currently accepted. However: A. With music, other test signals (such as noise) and short duration signals (like transients) our ability to discern high frequencies diminishes. We use steady state sine waves in this case because it presents the best case scenario for success, which allows us to say with significant confidence that if (for example) your limit is a 19kHz isolated, continuous, steady state sine wave, frequencies higher than 19kHz (of equal amplitude) will be inaudible to you in any other circumstances. B. There have been many more tests/studies which effectively test the human audibility of high and ultrasonic frequencies and which used music rather than sine waves as the test material (HiRez vs CD tests for example). However, as they were not tests aimed solely/specifically at testing the frequency limits of audibility, your statement is strictly true though not, IMHO, generally true.
2. I can't speak for "most folks" but again "generally" I would disagree. When I was a lecturer in audio engineering, my colleagues and I informally blind tested first year students, the vast majority of whom were 18-20 year olds, in small groups, as part of the "Listening Skills" module. We tested about 300 a year and I was there for 6 years. The vast majority struggled beyond 17kHz and were out by 18kHz, a dozen or so made it to 19kHz, not one of the roughly 1800 tested could detect 20kHz. In the analogue days, the BBC restricted broadcast TV to 15kHz but for several years broadcast an accompanying 19kHz pilot tone. None of the tens of millions of viewers appeared to notice when it started, when it stopped or during the period. In fact, it wasn't until many years later (the early 90's I believe), when some BBC broadcast engineer mentioned it, that anyone was aware it had ever occurred.
3. It's not difficult to measure phase shift, although it is difficult to measure the human perception of positioning from it, not least because that perception varies with frequency (and amplitude). Therefore, we don't know THE answer because there is no one answer. What we do know is that phase shift which affects positional perception is typically in the millisecond range and with best case test signals can extend down to the microsecond range. If we take any perception at all (not necessary just perception of positioning) of timing/phase then we're down into the hundreds of nano second range but still hundreds of times above what any moderately competent DAC should achieve.
4. This is the most obviously incorrect statement, although I'm not a mathematician and so might be mistaken. As I understand it, Nyquist's theory does not mention or assume sine waves, in fact it does not consider continuous signals of any type. The actual Sampling Theorem (which describes and proves the Nyquist frequency), also does not assume a sine wave, it assumes any mathematical function which has a Fourier transform, EG. All acoustic sound waves (regardless of complexity), which obviously does include all music! In fact, in his seminal 1948 paper "A Mathematical Theory of Communication" (the paper which proved the sampling theorem and why it is commonly called the Nyquist/Shannon Sampling Theorem), Shannon specifically states: "
A communication system is designed not for a particular speech function and still less for a sine wave ...". From what I understand (which is admittedly limited) of the mathematical contributions to the sampling theorem, rather than say "virtually all the math ... assumes a continuous sine wave", I would say the opposite; none of the math assumes a sine wave! I'm not however disputing that many of the explanations/demonstrations of the sampling theorem use a single continuous sine wave as an example.
5. Although Shannon/Whittaker's perfect interpolation formula is a sinc function, the maths which explain how a modern DAC works does not, as far as I'm aware, assume this perfect sinc function, which is impractical to implement. Therefore other math (which doesn't assume a perfect sinc function) has been developed to get around the engineering practicalities. While I agree that a DAC is effectively approximating, we have to be very careful as the word "approximate" is both relative and frequently abused. Every work of engineering has a practical limit of accuracy, so the question isn't whether a DAC is approximating, it's by how much. With modern technology, even cheap DACs can/should be astonishingly accurate, with any approximations (interpolation errors) being well below audibility.
Again, this is NOT intended as an attack, I'm not even disputing your observations, just some of your wording/rationale suggesting an explanation for those observations. For example, with the first two sentences I've quoted; I'm not disputing your observation and I obviously can't dispute what those observations may suggest to you personally. However, what it suggests to me is not that "we" (science) doesn't know everything yet but that "we" (personally) don't know how the manufacturer/s are actually implementing their filters. It seems to me far more likely that some DAC manufacturers, especially those offering filter choices, maybe implementing filters deliberately designed to be audibly distinguishable. In all fairness, you do imply this possibility in a subsequent post. I think we need to be very careful, particularly here on head-fi, not to appear to invoke, support, rationalise or add fuel to the fire of audiophile myths. Just sayin'
G
