Topic: Resample to 44.1 or record at 44.1 (midside Q)

[Will_S]

Edit:  Imperfect analogy:  Does having 3 points define a line any better than 2 points?

The answer to your analogy is yes, 3.

You think two points are inadequate to define a straight line (not a line segment, a line)?

Actually I suppose more points might help, if there was noise in the position of the individual points vs the line they describe. Is that what you meant? 

[DSatz]

prof_peabody, your analogy leaves out something very important. Can I have a moment to explain it in a roundabout way? You are asking excellent questions but the method of visual imagery which you (and about a million other people) are trying to get answers from can't possibly do the trick.

Let me suggest that you consider the analog signals going into the digital recorder, the analog signals that come back out in playback, and a third analog signal: the output subtracted from the input--a/k/a the difference or change or error (a/k/a noise and distortion) caused by the recorder's imperfections.

We're trying to identify the inherent limitations of sampled representations of continuous waveforms, so let's make an "assumption for the sake of argument" that the converters in this recorder are as linear and quiet as they can ever be. We want to know which flaws are inherent to the process, and can't be overcome by better converters, better analog circuitry, better flashing lights or generally, by spending more money.

OK. To start with, of course one full cycle of a low-frequency waveform will be sampled more times than one cycle of a high-frequency waveform will be. But it's a mistake to conclude that the low-frequency waveform is getting a better description as a result. The conventional visual analogy breaks down completely on this point, and gives a wrong answer. What tells the truth is the analog "difference" or "error" signal that I mentioned earlier. In a well-implemented digital recorder, the magnitude of the "difference" or "error" signal will be about the same for the high-frequency waveform as it is for the low-frequency waveform.

That isn't a hypothetical statement. Almost everyone in this forum has the equipment and/or software to create "error" signals of this kind. They can be observed and measured by anyone, and indeed have been listened to and looked at and measured for decades. Doing so can be a big "oh!" moment for understanding digital recording. It's the real-world fact, and any mental models that we construct to help ourselves understand the process must take it into account.

So where does the "three data points vs. fifty data points" model go off the tracks? You might see something very interesting (but probably not hear it) if you could remove the anti-aliasing filters from your digital recorder. Nowadays they tend to be an integral part of the D/A converters, but in the early and mid 1980s when digital recording first entered the recording studios, they were physically separate components (though usually on the same circuit board). Those D/A converters really did deliver the stepped waveforms that many people imagine are at the output of a digital audio recorder; then the filters smoothed those waveforms out (though not just by simple linear interpolation as many people seem to imagine).

Still, you could insert a probe in between the two components and look at the D/A converter's direct output. And if you did that, and if you created an "error" or "difference" signal at that point, you'd see that the "difference" or "error" signal on high frequency inputs would have a different frequency spectrum from the corresponding error signal for low frequency inputs. Probably there would also be some difference in magnitude, just because nothing's perfect. But the main energy of both error signals would fall above the "one-half the sampling rate" frequency--and not incidentally, above the range of human hearing. So the anti-aliasing filter would leave you with smooth sine waves at both frequencies, if that's what you'd put in.

--best regards

P.S.: A closely related issue is low-level vs. high-level signals. A full-scale waveform is "described" with the full range of sample values--for a 16-bit system, all 16 bits are used, etc.--while a low-level waveform (say, at -60 dBFS) exercises far fewer bits. The "connect the dots" model predicts that the low-level signal will be less accurately represented, and will therefore have much greater distortion. Yet with any well implemented digital recorder this doesn't occur--a fact which it's not at all difficult to show nowadays.

[prof_peabody]

So where does the "three data points vs. fifty data points" model go off the tracks? You might see something very interesting (but probably not hear it) if you could remove the anti-aliasing filters from your digital recorder. Nowadays they tend to be an integral part of the D/A converters, but in the early and mid 1980s when digital recording first entered the recording studios, they were physically separate components (though usually on the same circuit board). Those D/A converters really did deliver the stepped waveforms that many people imagine are at the output of a digital audio recorder; then the filters smoothed those waveforms out (though not just by simple linear interpolation as many people seem to imagine).

Still, you could insert a probe in between the two components and look at the D/A converter's direct output. And if you did that, and if you created an "error" or "difference" signal at that point, you'd see that the "difference" or "error" signal on high frequency inputs would have a different frequency spectrum from the corresponding error signal for low frequency inputs. Probably there would also be some difference in magnitude, just because nothing's perfect. But the main energy of both error signals would fall above the "one-half the sampling rate" frequency--and not incidentally, above the range of human hearing. So the anti-aliasing filter would leave you with smooth sine waves at both frequencies, if that's what you'd put in.

So how good are the filters at smoothing?  There are many implementations of these filters right?

The interpolation of the points is not perfect - ie, it doesn't perfectly represent the input signal.  If you sample at a slightly higher rate, you leave yourself less prone to interpolation error.

Playing with sine waves isn't necessarily helpful as well - 3 points to describe one sine wave will have a unique solution...

From a political standpoint - the jury is still out on the sample rate issue.  There are papers both for and against using higher sample rates, and many experts who back each viewpoint.

[DSatz]

> The interpolation of the points is not perfect - ie, it doesn't perfectly represent the input signal.  If you sample at a slightly higher rate, you leave yourself less prone to interpolation error.

You're jumping to a completely false conclusion about sampling at higher rates and what you call "interpolation error." If your beliefs were correct, a 5 kHz tone recorded at some relatively normal level with 44.1 kHz sampling would show distinctly greater distortion in playback than the same tone recorded at the same level with (say) 96 kHz sampling.

Similarly if you doubled the frequency to 10 kHz, according to your beliefs the distortion (in a 44.1 kHz system) would increase considerably as compared to what you got at 5 kHz. The closer you came to the upper limit of the system the greater the distortion would have to be, because fewer samples are taken per cycle.

In the real world, however, none of the above generally happens. Hmmm ...

One definite confusion factor is your use of "one cycle of a wave" as your yardstick rather than a set period of time. Given a constant clock speed, of course a lower-frequency waveform will get more samples during the interval that your mind's eye is allotting to it. So you're not using a "level playing field," and that misleads you somewhat.

Apparently it's difficult for most people to visualize what anti-aliasing filters do without oversimplifying them. So I say skip that and go by the quality of the signals that come out of the filters. For audible purposes, who cares what the signal looks like prior to the output filters, as long as a clean enough signal emerges from them.

It would be a mistake to point to the shape of a signal that no one ever hears, and complain that it doesn't look beautiful in your mind's eye.

--best regards

[SmokinJoe]

The interpolation of the points is not perfect - ie, it doesn't perfectly represent the input signal.  If you sample at a slightly higher rate, you leave yourself less prone to interpolation error.

This seems like a reasonable statement, and perhaps to a point it is.  This is why your A/D converter probably oversamples at 128times as fast as 44.1k.  Then it has the filters and the data to decide the best way to produce a 44.1k result, and it does a great job.  But making an assumption that you should sample at 48k and then try to convert from 48k to 44.1k on a computer without the filters and the 128x oversampling, this is where the assumptions fall apart IMO.  The best approach is simply to record at the rate you want in the end.  Conversions are the real compromise, because there you don't have extra data and RE-interpolation error is a problem.

[prof_peabody]

> The interpolation of the points is not perfect - ie, it doesn't perfectly represent the input signal.  If you sample at a slightly higher rate, you leave yourself less prone to interpolation error.

Well, nothing in this world is absolutely perfect. But you're jumping to a completely false conclusion about sampling at higher rates and what you call "interpolation error." What an anti-aliasing filter does is critical to the overall result, and deserves to be understood factually (or conversely, maybe not so well understood but accepted, once its actual behavior has been determined).

Since you mentioned politics: It's not that there can be no benefits from higher sampling rates. I know of no one who actually says that--though it's the position which most advocates of higher rates argue against, as if it were commonly held. That kind of "straw man argument" muddies the discussion a lot sometimes.

But please consider: If your assumptions were correct, a 5 kHz tone recorded at some relatively normal level with 44.1 kHz sampling would show distinctly greater distortion in playback than the same tone recorded at the same level with (say) 96 kHz sampling. Similarly, if you doubled the frequency to 10 kHz, then according to your theory, the distortion in a 44.1 kHz system would increase considerably, as compared to what you got at 5 kHz. The closer you come to the upper limit of the system, the greater the distortion would be.

So check it out. In the real world, none of the above stuff usually happens. Hmmm ...

One definite confusion factor is your use of "one cycle of a wave" as your yardstick rather than a set period of time. It's a truism that the lower the frequency, the longer the cycle of its waveform. Given a constant clock speed, of course a lower-frequency waveform will get more samples during the longer interval that your mind's eye is allotting to it. So you're not using a "level playing field," and that misleads you somewhat.

Also it may be impossible for most people to visualize what anti-aliasing filters do without oversimplifying them. Parts of the relevant math are beyond me, so I go by the quality of the signals that come out of the filters. All filters are imperfect, but some imperfections are audibly acceptable while others are not. We can decide by listening, by measurement, or (preferably) both.

Please consider that for audible purposes, it would be OK if a signal looked dreadful prior to the output filters. It could be loaded with crap above the cutoff frequency, as long as a clean enough signal emerges from the outputs. It would be a mistake to point to the shape of a signal that no one ever hears, and complain that it doesn't look beautiful in your mind's eye.

--best regards

A couple points:

- Why are you invoking an anti-alias filter?  It has very little to do with the questions I posed.  You can low pass to 10 kHz (for example) and still go through the logic I presented in my earlier posts.  I consider this an effort to change the topic to avoid answering the question.  Aliasing does not need to be discussed to answer the questions.

- even if one changes the "yardstick" to a set period of time you still encounter the same predicament I presented in the initial post (in fact time and frequency domains are directly related - you can use a Fourier transform to see this for yourself).  As the input frequency approaches the half the recording frequency (or if you want the frequency limit imposed by the anti-alias filter before the ADC), the number of samples that define the wave at a given frequency decreases.  As the number of sample decreases, you rely more heavily on interpolation algorithms to recreate the waveform in a DAC. 

[prof_peabody]

The interpolation of the points is not perfect - ie, it doesn't perfectly represent the input signal.  If you sample at a slightly higher rate, you leave yourself less prone to interpolation error.

This seems like a reasonable statement, and perhaps to a point it is.  This is why your A/D converter probably oversamples at 128times as fast as 44.1k.  Then it has the filters and the data to decide the best way to produce a 44.1k result, and it does a great job.  But making an assumption that you should sample at 48k and then try to convert from 48k to 44.1k on a computer without the filters and the 128x oversampling, this is where the assumptions fall apart IMO.  The best approach is simply to record at the rate you want in the end.  Conversions are the real compromise, because there you don't have extra data and RE-interpolation error is a problem.

Do you have any information that shows the ADC chip initially samples at ~5600 kHz?  I'm not sure this is the case - that's why I'm asking.

[SmokinJoe]

Do you have any information that shows the ADC chip initially samples at ~5600 kHz?  I'm not sure this is the case - that's why I'm asking.

128x oversampling was considered "state of the art" in 2000, and they played it up big time back then. 5.6 Mhz sample clock = 128x 44.1khz, and 6.1Mhz sample clock will give 128x oversampling at 48k.  I suspect a modern (now obsolete?) Mini-Me or V3 will do this, but I don't know.  Now that a lot of devices will do 96k and 192k, I suspect the sample clock rates are the same and you get 64x and 32x oversampling at those high rates.  Rather than explain that, they just don't brag about it.

Here is a  device which claims 128x oversampling.  Not exactly "state of the art".
http://www.midi-store.com/M-Audio-Flying-Cow-24-bit-D-A-and-A-D-Converter-p-16880.html

Chipset from April 2000 showing 5.6Mhz and 6.1Mhz sample clock.
http://www.asahi-kasei.co.jp/akm/en/product/ak5393/ak5393_f04e.pdf

Others:
http://recforums.prosoundweb.com/index.php/t/14013/0/ (2004 geek discussion)

Here is a story where they are debating in 2002 what we are still debating here today 
http://emusician.com/daw/emusic_bridging_gap/

[prof_peabody]

Do you have any information that shows the ADC chip initially samples at ~5600 kHz?  I'm not sure this is the case - that's why I'm asking.

128x oversampling was considered "state of the art" in 2000, and they played it up big time back then. 5.6 Mhz sample clock = 128x 44.1khz, and 6.1Mhz sample clock will give 128x oversampling at 48k.  I suspect a modern (now obsolete?) Mini-Me or V3 will do this, but I don't know.  Now that a lot of devices will do 96k and 192k, I suspect the sample clock rates are the same and you get 64x and 32x oversampling at those high rates.  Rather than explain that, they just don't brag about it.

Here is a  device which claims 128x oversampling.  Not exactly "state of the art".
http://www.midi-store.com/M-Audio-Flying-Cow-24-bit-D-A-and-A-D-Converter-p-16880.html

So if you read the specs the 128 X oversampling is a sigma delta filter, which means it's probably 128X at a 1 bit resolution.  Nice try...

Chipset from April 2000 showing 5.6Mhz and 6.1Mhz sample clock.
http://www.asahi-kasei.co.jp/akm/en/product/ak5393/ak5393_f04e.pdf

Again - 128X oversampling using a sigma delta filter at 1 bit resolution.

Others:
http://recforums.prosoundweb.com/index.php/t/14013/0/ (2004 geek discussion)

Here is a story where they are debating in 2002 what we are still debating here today 
http://emusician.com/daw/emusic_bridging_gap/

So in all the links you provided the over sampling is achieved through a sigma-delta, 1-bit filter. 

Thanks for playing.

edit: so in essence the oversampling involves doing the ADC to essentially a DSD format and then you convert that signal to 16 bit / 44.1 khz.  You'd have to do a lot of math the work out how much oversampling is really being done...  It's not as much as you think.

edit2: I forgot to mention that using a delta-sigma technique in an ADC usually does great noise shaping and often means you don't need an anti-alias filter

[SmokinJoe]

I'm not qualified to debate what A/D methodology is better than another.  I have a little understanding, but I get lost in the math.  I never meant to imply that they are doing a full 24bit value calculation at 5.6Mhz.  What I did mean is that here is a great tool, designed to do what it does, and I think it's best to let it do it's thing.  I think the original question 3 pages back was "should I record at 44.1, or record at 48K and resample on the computer".  I say, record at 44.1k.

~~~~~~~~ next day ~~~~~~~~
I was curious, so looked this up.  According to the manual, a Korg MR1000 recording 1bit DSD at 5.6mhz will fill 1 GB file in 11 minutes.  A 24/192 file is 13 minutes....  so 1bit at 5.6mhz is something like (HUGE generalization here) something like 24/226khz if such a beast existed.  So at 192khz, there isn't much oversampling.... agreed.

Again, my point is that the A/D has the information to prune that down to 44.1k better than a computer does, starting with 48k or 96k.