Hi elstude. I'm sorry for what I have for a long time did not respond to questions. I just have no experience of commenting on the CA and I wanted to wait and see what the discussion will go in the direction. The very title of this article lies the whole essence of what I wanted to discuss on the forum. Unlike "static" characteristics (spectral and dynamic domains), which are often discussed, I would like to emphasize the importance of what we hear in real time from our acoustic system - to "dynamic" characteristics (temporal and spatial domains ). And especially I like to emphasize the importance of temporal resolution for emotional perception when listening of music.
And it has nothing to do with the digital aspect. I was not going to oppose an analog (vinyl, tape) and digital (CD, Hi-Res). Just what we hear from our speakers. This temporal resolution It may be worsened by your speaker or the speaker cables or phono preamp, or cartridge, ... Any component can "slow down" transients. Just what I wanted to say.
Only once, I noticed that the CD format is not enough to reconstruct high time domain, also citing in this context (Art Dudley and Rob Robinson). But you are brought down to me hurricane criticism. All about what you say - it properly. It is generally accepted and does not require a large discus. But, once again I ask - how it relates to the topic of this article?
Now a substantive response to your first question on this topic:
It seems that temporal accuracy and temporal resolution are being confused here. Accuracy is a given, and for the sake of argument can be as high as one wishes - picoseconds, femtoseconds, etc.. When someone says a CD samples "accurately" to the picosecond level (that is, the sample clock is stable and has low jitter), that may be true, but that has nothing to do with the temporal resolution. The distinction between accuracy and precision / resolution is one of the prime topics emphasized early in college introductory physics and chemistry (or even grammar school advanced placement classes in the same subjects): the difference between accuracy and precision are critical in science and easily confused unless one has had experience or training in the subject.
Take two balance scales that are, let's say, 100% accurate. One weighs to a precision (almost the same thing as resolution) of 1 gram, the other 10 grams. Put a 10 gram mass on both scales, they will both indicate 10 grams, with perfect accuracy. Place a 12 gram mass, the more *precise* of the two scales will indicate 12 grams. Remember both scales are 100 percent accurate - but you can't expect the second scale to resolve 12 grams, because it is below the measurement *precision* of the scale. The second scale will "accurately" report 10 grams for the 12 gram mass - within a resolution of +/- 5 grams. So, at best, you know that your measurement of the mass is 10 grams plus or minus 5 grams. A 16 gram mass would be measured as 16 grams on the first scale, 20 grams on the other, etc. The second scale is accurate, but only within the specified precision. On the other hand, a scale that is not "accurate" would have some discernible error in the measurement. For example, the scales report 11 and 20 grams in the first measurement - though the resolution is the same. For the optimum result, we need both good accuracy *and* precision.
Now take the CD sampler accurate to 1 picosecond, given as an example. Yes, sample after sample are within one picosecond of the sample period (or even better is possible, with a super low jitter clock). But it simply cannot accurately resolve signal events with a temporal precision greater than the sample rate - approximately 23 microseconds (rounding to the nearest microsecond; 1/44100 is actually a transcendental number which can be represented to an arbitrary precision depending on the number of decimal places, which we don't care about here). So an event occurring at a given time can be resolved with certainty at best with a temporal resolution of roughly 23 microseconds. If you increase the sample rate to 192 kHz the temporal ACCURACY may be the same (at the same time coordinate, with the same picosecond or femtosecond accurate clock) but the temporal RESOLUTION is more than 4 times better - about 5 microseconds. (or to be precise, 5.2083333 microseconds with the 3 repeating on and on and on).
Temporal resolution is defined by the sample rate.
Taking an extreme example for illustration of a boundary condition, if the brain and auditory system only resolved sounds with TEMPORAL resolution at the second (1,000,000 microseconds) level, this would be problematic because a threat to survival such as a leopard pouncing from behind would not be detected as readily. Imagine an experiment where we played a sound of an animal springing for two human test subjects, from a loudspeaker positioned some moderate distance behind and above the subject. On the one hand the sound is sampled at 10 Hz. On the other we sample at 192 kHz. The first case has a TEMPORAL resolution of 100,000 microseconds (0.1 second), the other about 5 microseconds. Do you think that in both cases both subjects will be able to react in the same way, including detecting the position of the sound, to each stimulus? From the argument presented in one of the responses here one should be able to reconstruct the original waveform from the lower sample rate signal, ergo both subjects by the argument presented would be expected to react identically. Of course, I am saving the red herring, which is due to the fact that the 10 Hz sampled signal will be antialias filtered, removing frequencies above 5 Hz - so there would be nothing in the audio to react to! But the argument presented is that somehow one can reconstruct a signal by calculating the intersample waveform. The problem is there is no way "in the universe" to reconstruct the ORIGINAL "leopard pouncing" signal via such an operation.
There is absolutely no way that a signal sampled at a given sample rate to a digital waveform has the same temporal resolution as a signal sampled at higher sample rates. If it did, then all the research labs in the world (using high speed analog to digital converters for signal sampling and recording) could just go and throw away all of our expensive high speed digital sampling hardware. Same thing with our 100 GHz sampling oscilloscopes. Why waste all that money when a 100 MHz scope has putatively the same temporal resolution? Because it does not.
If a paper were submitted for publication to a peer reviewed technical journal and reported conclusions which depended on sampling a signal and the paper tried to infer that an event was determined to occur with a temporal precision greater than the sample rate, the paper would be rejected, with a suggestion to repeat with a more capable experimental measurement (that is, appropriate sample rate). Any argument that the original signal (that is, containing events faster than the sample rate) could be reconstructed perfectly from a lower sample rate signal would be ridiculed. There is absolutely no way this information could be extracted from a measurement made at a lower sample rate - which has lower TEMPORAL resolution. If the whole reaction we're trying to observe takes place in 100 nanoseconds and we can only sample at 1 microsecond, then we won't measure anything useful, let alone could we expect to somehow reconstruct the same data set that one would obtain at higher temporal resolution (sample rate).
One cannot reconstruct an ORIGINAL signal containing spectral content at frequencies above half the sample rate, from one sampled at a lower sample rate, just because "there is only one (such) signal in all the universe," because the signal bandwidth of the "one signal in the universe" that fits the points has already been band limited by the antialiasing filter, and parts of the original signal discarded. The signal you get at the lower sample rate **only corresponds to band limited version of the original signal** - which is NOT the same as the original signal. There isn't any way to determine the ORIGINAL signal without sampling at a higher rate in the first place. You can certainly calculate the sample position at arbitrary inter-sample time intervals, but that will not give you the same result as sampling the ORIGINAL signal at a higher rate. Sure, one could sample the *band limited* signal at a higher rate, and in that case the result will be exactly the same - but there would be no practical reason to oversample (as in analog to digital conversion) a (severely, in the case of analog to digital conversion) band limited signal in the first place. The scenario with analog involves ORIGINAL signals which also are band limited; in the real world, all signals are band limited to some extent - it's a matter of the criteria applied; but analog is band limited to a much lesser extent than digital, and the characteristics of the band limiting are also quite different.
Any signal which is lowpass filtered to prevent aliasing at lower sample rates is going to have a greater variation in group delay / phase shift near a fixed signal frequency (say, always at 10 kHz) than a signal sampled at a higher sample rate, presuming the antialias filtering is chosen appropriately for the sample rate (and it would always be, otherwise one wouldn't go to the trouble of using higher sample rates). A signal reproduced on a vinyl LP sourced from analog sources doesn't encounter the brickwall filter used in analog to digital converters / CDs. There is a high frequency roll off, but it is a gentle 6 dB per octave above the cutter head resonance of typically 50 kHz. By comparison the brickwall filter used to record CD format audio has a much steeper slope, about 100 dB of attenuation in a small fraction of an octave (antialiasing filters aren't even expressed in terms of dB per octave; just passband, stopband, ripple and attenuation). Furthermore, compared to our analog 6 dB per octave rolloff, there is a much greater phase shift variation among frequencies in the sampled signal. And just above about 20 kHz, there is NO signal left; on the other hand with analog, and vinyl, there is considerable signal energy, continuing for octaves above. And that is a key difference between analog and digital. So, in digital recording, we try to get closer to the TEMPORAL characteristics of analog by increasing the sample rate and pushing our brickwall filter higher and higher in frequency, so that the disruption of time relationships / coherence between the frequencies comprising our audible frequency range (up to 20 kHz, more or less) audio is minimized. Then, our music signal (or sound of the panther pouncing) is reproduced with the temporal relationships between different frequencies closer to (if not entirely preserved) compared to the actual sound found "in nature" and accordingly our auditory system / brain / emotional state responds more favorably by comparison. "Engaging, toe tapping, PRAT." As a bonus we can enjoy knowing about the technical elegance of capturing more of the frequency range of analog (and vinyl LPs) which extends strongly at least two octaves above the bandwidth limit of a CD (as proven by many measurements using spectrum analysis of signals from LPs, including those referenced in the post).
Sorry for the long post.
Pure Vinyl Club