Interesting question, Mapman, but I don't think that it has an answer.
Since there are a great many ways in which each medium and its reproduction can be inaccurate, how does one weight each of those ways relative to the others, and tally up a net balance?
Even if such a tradeoff could be worked up in a comprehensive manner, it seems to me that the weightings and the net result would vary as a function of the music, the recording, the system, the room, and the listener.
I assume, btw, that you are referring to accuracy with respect to the recording, as opposed to some envisionment of the original event (which would be, and as you probably recall has been, a whole separate discussion).
Best regards,
-- Al |
i figure analog is seeing as how digital is a sampled representation. sampling (digital) can be accurate but it's inherently less complete. there are gaps. Digital is but a sample of the sound. Analog is the entire sound. Although these statements reflect a commonly held position, as I see it they amount to assertions that because digital does not have an infinitely high sample rate, and an infinite number of bits per sample, it is inherently inferior to analog. As I see it, given that analog has many shortcomings of its own, and given the fact that our hearing mechanisms are not infinitely resolving, there must be some finite value of those parameters which will, when implemented in well designed hardware, inarguably result in digital being the superior format. Whether or not that point has already been reached, or is foreseeable, is debatable. But I don't think the fact that digital is a sampled format in itself has much if any relevance to that debate. Regards, -- Al |
Nil, yes the number of samples (for each cycle of each frequency component of the analog signal that is being digitized) increases as you described, as the analog signal frequency decreases. Hi rez also increases the number of samples per cycle. For instance, a 192 kHz sample rate provides 192/44.1 = 4.35 times as many samples as redbook cd's 44.1 kHz sample rate.
However, what is often not recognized is that the problem with having a finite sample rate and a relatively limited number of samples of high frequency components in the signal is not "gaps," per se. In theory, if an infinitely long analog waveform is digitized using a sample rate that is at least twice the frequency of the highest frequency component of the analog signal, and if the number of bits per sample are high enough to reduce what is called "quantization noise" to insignificant levels, the digital data can be converted back to analog perfectly, with no loss of information in the "gaps."
Arguably the most significant theoretical issue, however, is that frequency components in the original analog signal that equal or exceed half the sample rate MUST be kept out of the a/d converter, or they will be reconstructed following d/a conversion as spurious lower frequencies (referred to as "alias frequencies"). Keeping those frequencies out of the a/d converter, while at the same time avoiding side-effects on audible frequencies, has historically been one of the most major technical challenges in digital. Hi rez formats certainly have a big advantage with that issue, all else being equal, as 96 and 192 kHz exceed twice the highest audible frequency (nominally 20 kHz x 2 = 40 kHz) by a far larger factor than redbook's 44.1 kHz.
Best regards,
-- Al |
11-04-11: Hevac1
When recording say a violin, is the first sample taken at the start of a note played and does it also sample at the very end of the note regardless of the samples in between? If it does not then how can digital play back components perform proper decay and bloom of the music played regardless of the sample rate? There is no synchronization between the start or end of a musical note, or anything else involving the timing of the music, and when the samples are taken. But keep in mind that notes don't start infinitely fast, and don't end with infinite abruptness. The speeds that are involved correspond to the highest frequency components of the note. If all frequency components that are audibly perceptible can be captured with sufficient accuracy (whatever that may mean), then nothing is lost. If I sit and play an instrument for recording purposes onto an analog tape I will record all that I play. Is this also true for digital recording or is the device recording parts of the sound (sampling) I am playing and the computer puts it together sort of like digital morphing of one image to another. It will record (and the digital data will contain) all that you play, but only up to around 20kHz, and with accuracy that is less than perfect in a number of ways (quantization noise reflecting the finite number of bits per sample, frequency response ripple and phase shifts resulting in part from the low pass filtering that must precede the a/d converter to prevent aliasing, etc.). The d/a conversion process does not, at least conceptually, involve adding information, combining images, interpolating between samples, or anything along those lines. Conceptually, once the digital data for each sample has been converted to a corresponding voltage it just involves REMOVING (filtering out) ultrasonic (higher than 20kHz) frequency components that are present in combination with the musical information (at frequencies below 20kHz). It is the presence of those ultrasonic spectral components that are what distinguish a sampled waveform from a continuous non-sampled waveform containing the same information. Your questions are good ones, though, as it's all pretty counter-intuitive. Good answers from Ralph & Mapman, also. Regards, -- Al |
Ralph, what do you feel is the more significant limiting factor for redbook, sample rate or bits per sample? Just curious.
FWIW, my instinct has always been that sample rate is the more significant issue, at least for most music. In fact I've been amazed at times at how good SOME cd's can sound, given the seemingly absurd 10% margin with respect to the Nyquist rate.
Best regards,
-- Al |
11-07-11: Atmasphere
My guess though is that when we can do 64-bit DACs on a regular basis that digital will start demonstrating the promise that its been showing. Thanks, Ralph. It seems to me, though, that it would be a pretty safe bet that that will never happen. In fact I suspect it is theoretically impossible, due to Johnson noise, shot noise, etc. Quantization of a 2 volt full-scale range into 64 bits would mean that the least significant bit corresponds to about 0.0000000000000000001 volts. (That's 18 zeros between the decimal point and the "1"). Intuitively it seems to me that although as you say the Nyquist theorem assumes unlimited resolution of the samples, 24 bits or so should be precise enough to be just as good for all practical purposes. Best regards, -- Al |
16 bits specifies 65,536 levels, approximately 0.00146 decibel per level. Actually it shouldn't be looked at that way, because the CD medium uses linear encoding, while the db scale is logarithmic. For example, the difference in db between the maximum possible value as represented digitally (65,535 as expressed in decimal form) and one "level" less than that (perhaps more properly expressed as one LSB increment less than that, referring to the voltage increment corresponding to the Least Significant Bit) is: 20log(65535/65534) = 0.000132 db In contrast, the difference in db between a value of 1 LSB increment above zero and a value of 2 LSB increments above zero is: 20log(2/1) = 6.02 db. So the number of "db per level" varies very widely depending on the specific levels that are being considered. What's the smallest level change the human ear is capable of discerning? What matters in this context is not the perception of changes in level, but our ability to perceive, among other things, differences in the RELATIVE amplitudes of the harmonics and other spectral components that collectively constitute a note. Our hearing mechanisms are far more sensitive to those kinds of differences, which affect timbre for one thing, than they are to simple volume changes. Speaking more generally, many of the recent posts in this thread have been excellent, IMO. Too many to cite individually. Ralph's point about analog hiss being much less objectionable than its digital counterpart (quantization noise resulting from the limited number of bits per sample), is a very good one of course. It should be mentioned, though, that careful application of dither in the digital recording process can go a long way toward minimizing that issue. And along the lines of Ralph's comment, careful "normalization" of volume levels during the recording process can minimize or eliminate the extent to which bits are sacrificed as a result of, for instance, overly conservative headroom allowances. It should also be pointed out that the 110db or so of dynamic range that a high quality analog tape machine may be able to provide is considerably greater than what can be put onto and retrieved from vinyl, as well as being more than what can be supported by most listening environments, and more than what is required by most music. A bottom-line point, IMO: Although I haven't yet gotten into hi rez, my suspicion, given how good SOME redbook cd's can sound, is that 24/192, if well implemented in both the recording and playback parts of the chain, should be good enough to deliver digital's full potential, in terms of perceived accuracy (which is the subject of the thread). On the other hand, the subjective preferability of that potential vs. vinyl at its best is another question altogether, about which opinions will obviously differ. Best regards, -- Al |
Hi Sam, This Wikipedia article appears to address your questions much more knowledgeably than I could. Some excerpts: Because of the nature of sigma-delta converters, one cannot make a direct comparison between DSD and PCM. An approximation is possible, though, and would place DSD in some aspects comparable to a PCM format that has a bit depth of 20 bits and a sampling frequency of 96 kHz.[3] PCM sampled at 24 bits provides a (theoretical) additional 24 dB of dynamic range....
DSD's dynamic range decreases quickly at frequencies over 20 kHz due to the use of strong noise shaping techniques which push the noise out of the audio band resulting in a rising noise floor just above 20 kHz. PCM's dynamic range, on the other hand, is the same at all frequencies. (Some high-end SACD players employ an optional low-pass filter set at 30 kHz for compatibility and safety reasons, suitable for situations where amplifiers or loudspeakers cannot deliver an undistorted output if noise above 30 kHz is present in the signal)....
The Korg MR-1000 1-bit digital recorder samples at 5.6 MHz, twice the SACD rate. It's also referred to as DSD128 because of the sample rate 128x that of CD....
There has been much controversy between proponents of DSD and PCM over which encoding system is superior. Best regards, -- Al |
11-08-11: Almarg
The difference in db between the maximum possible value as represented digitally (65,535 as expressed in decimal form) and one "level" less than that ... is:
20log(65535/65534) = 0.000132 db
A slight correction to this statement in my earlier post. Since a sign bit is involved, which defines + or -, the range of possible values expressed in decimal form is -32,768 to + 31,767. So the quoted equation should be: 20log(31767/31766) = 0.000273 db Regards, -- Al |
01-24-12: Terry9
A sine wave must be sampled 250 times to achieve 5% RMS distortion or less ... With all due respect, as someone who has taken several advanced courses dealing with digital sampling theory, and has designed digital circuits implementing FFT's and other digital signal processing functions, I have never before encountered such a statement. Are you sure you are not confusing sampling with quantization? Are you sure you are taking into account the low pass filtering or other techniques that are used to reconstruct the analog waveform during the d/a conversion process? In any event, can you provide some supporting documentation or rationale for that claim? Regards, -- Al |
Hi Terry,
It seems to me that the flaw in that analysis, as my previous post intimated might be the case, is that it does not take into account low pass filtering that is applied in the d/a process to smooth out the stepped character of the sampled waveform.
Essentially, your distortion percentage is incorporating ultrasonic spectral components that represent sampling artifacts (as opposed to distorted musical information), which ultimately get filtered out.
Another way to look at it is that were your claim true, then for redbook cd an audio frequency of 44100/250 = 176 Hz would be distorted by 5% when it is played back, and higher frequencies would be distorted by a far greater percentage than that. Clearly the cd medium, while far from perfect, does better than that!
Regards,
-- Al |
Hi Terry,
Rather than getting into a lot of esoteric mathematics that would be necessary to provide a quantitative perspective on all of this, Ill just make a couple of additional qualitative points. I suspect that following your rebuttal we'll then, as you say, have to agree to disagree.
I agree that the low pass filtering/analog reconstruction process cannot be done to absolute perfection. However, consider the spectral components that distinguish an audio frequency sine wave from that sine wave as sampled at 44.1 kHz. The spectral components that distinguish those two waveforms are all at ultrasonic and RF frequencies, and as such are essentially inaudible to us. (The reason I say essentially is that, as you may be aware, some seemingly credible studies have suggested that we may be somehow able to sense the presence of frequencies up to perhaps as high as 100 kHz if they are accompanied by frequencies that are within the nominal 20 kHz range of our hearing). Consider especially the spectral components corresponding to the transition times between steps. Those are at radio frequencies!
Yet in referring to them as distortion, and citing that distortion as the basis for defining the threshold of sample rate acceptability, your analysis implicitly assigns audible significance to ALL of these ultrasonic and RF spectral components, little or no differently than if they were some low order distortion components lying well below 20 kHz. It also implicitly assigns audible significance to these ultrasonic and RF spectral components that is no different than if during the analog reconstruction process no filtering were applied to them at all.
Second, consider the hypothetical situation where an infinitely long sample record is available, with each sample having infinite resolution (i.e., zero quantization noise). The rationale behind your contention that 250 samples per cycle are necessary to achieve 5% distortion would seem to be no less applicable to that situation than it is to real world digital scenarios, despite the fact that (as I think you would agree) only a little more than 2 samples per cycle are necessary in that hypothetical situation.
The bottom line, IMO and with respect , is that I doubt your contention that a sample rate of more than 100x the Nyquist rate is necessary to achieve reasonable (although still high!) levels of distortion would be likely to receive widespread support even among the most ardent vinyl advocates, or at least those among them who have sufficient technical background to comprehend the issues.
Regards,
-- Al |
Hi Terry, I agree with your aside concerning filtering, but, would you not agree that every capacitor introduces distortion? And that therefore we should be concerned with physical measurements rather than idealizations? Absolutely. The various non-idealities of low pass filters, in both the recording and playback parts of the chain (anti-aliasing and reconstruction filters, respectively) are a major issue in digital audio. I also agree that the spectral components are all above 20KHz. Would you not agree that this creates a very rich ultrasonic environment? And further, that this is mainly generated from harmonies in a fairly narrow 4 octave range, suggesting that the ultrasonics are also clustered? I note that different frequencies "beat" against each other; e.g. 33KHz and 34KHz signals beat to form their difference, or 1 KHz. Further, these beats will be related to the fundamentals in no simple respect, producing distortions which have not been characterized. Agreed. In fact, arguably the most important reason for low pass filtering the d/a output is to eliminate (or at least greatly attenuate) beat frequencies that would otherwise arise as a result of non-linearities downstream in the system (and perhaps to some extent in our hearing mechanisms as well). Were it true that ultrasonic distortion was inaudible, SACD would be no improvement on CD, which is not observed. Therefore, I stand by the assertion that total distortion is what is important, until it is proved otherwise. As indicated in this Wikipedia writeup: Because of the nature of sigma-delta converters, one cannot make a direct technical comparison between DSD and PCM. DSD's frequency response can be as high as 100 kHz, but frequencies that high compete with high levels of ultrasonic quantization noise.[36] With appropriate low-pass filtering, a frequency response of 50 kHz can be achieved along with a dynamic range of 120 dB.[2] This is about the same resolution as PCM audio with a bit depth of 20 bits and a sampling frequency of 96 kHz. So although comparison between the parameters of the two formats is not straightforward or precise, it would seem clear that the performance of DSD is, at least potentially, superior to that of redbook cd in terms of dynamic range, and also in terms of providing greater margin relative to the Nyquist rate. That increased margin can be expected, at least potentially, to lessen the side-effects of anti-aliasing and reconstruction filters that may occur at audible frequencies, just as it can for hi rez PCM, relative to redbook PCM. In summary, I think that our positions are similar in a lot of respects, but we agree to disagree on the need for a sample rate that approaches the one you have advocated. My thanks to you, also, for a stimulating and mutually respectful discussion. Regards, -- Al |
01-31-12: Orpheus10
In addition, harmonics are always presented as a lower frequency affecting a higher frequency, but never how higher frequencies affect lower frequencies. I'm saying these higher, inaudible frequencies affect lower frequencies. Can anyone shed light on that. I'm not sure I understand the question. The character of what we hear is a function of the combination of fundamental frequencies, harmonics, and broadband spectral components that are present at any given time. As Learsfool and I stated, seemingly credible studies have indicated that frequencies that are significantly above 20 kHz can be sensed under some circumstances, particularly if lower frequencies are simultaneously present. 02-01-12: Orpheus10
When CD's came out, I bought them to hear the same music I had on LP, only better. One CD in particular was inferior to the LP, it lacked "nuance"; and as jazz lovers know "nuance" is everything.
I down loaded this LP to my computer, and on playback all the "nuance" was there; complete with record noise. What do you make of that? Orpheus, an obvious question: What makes you assume that the CD and the LP were mastered identically? Frogman, thanks very much the kind comment in your post of 1-26. Regards, -- Al |
