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Old 15th May 2012 | Show parent
Gear Guru
Verified Member
Hi Dan (and whomever is passing on his responses),

First, thanks for the extensive response!

Originally Posted by Lavrytech ➡️
Although most contemporary audio converters are a multi-bit sigma-delta based design; the fact that the modulator operates at much higher sample rates than the output sample rate does not mean that analog issues are not part of the reason why there is an optimal sample rate. And the fact that the modulator output undergoes digital processing does not mean there is no compromise at that stage of conversion.

Here is Dan Lavry’s response:
“The sigma delta modulator speed is determined by various technology tradeoffs. For example, the size of the many capacitors embedded in the IC is very limited. In fact, the modulator is optimized for the available technology. There are 3 main parameters – modulator speed, number of modulator bits and filter order. A given combination offers the ability to design a noise shaping structure.

Say you have a modulator operating at 6MHz, with 5 bits, and a fifth order filter. If you wanted to end up with 3MHz usable signal bandwidth, there is no room for noise shaping because 3MHz is already at the Nyquist frequency of the 6MHz front end. So the outcome is 5 bits quality (with 3MHz bandwidth). If the modulator were 1 bit, you have a 1 bit converter (to 3MHz). Neither of these examples is good for audio.

Now say you wanted to reduce the usable bandwidth to 1MHz. That enables some noise shaping – moving noise from the 0-1MHz range to the 1-3MHz range. The noise shaping will yield somewhat better performance for signals under 1MHz, while making the range over 1MHz not usable (that is where you send the noise to using noise shaping). Now let’s accommodate a 30KHz range. Clearly there is a lot more room for the noise shaping (30KHz to 3MHz) so the region under 30KHz can be made much better quality (more bits).

So once again, the end result for lower bandwidth ends up with better performance.

The tradeoff between speed and accuracy is alive and well inside the modulator, and the examples I used (charging caps and settling opamps) applies very well to those circuits. The slew rates inside the modulator are very fast and settling times are critical. The modulator speed is, as well as the combination of the rest of the modulator parameters are optimized for a given technology, and the modulator is a PART of the process. The end result is still the same; more speed (signal bandwidth) means less accuracy.”
I think I didn't make myself clear: I understand the points in your article about the analogue stages but I don't see how that applies to the practical world of modern multi-bit sigma-delta modulator converter designs. My point/question wasn't so much about the much higher rate of the modulator or the lack of any compromises in the digital conversion stages but rather about the fact that the modulator rate is constant for all target sample rates subdivisions of the modulator rate. If the target rate is 44.1 Khz, 88.2 Khz or 176.4 Khz, the modulator is always running at 5.6 Mhz. If the target rate is 48 Khz, 96 Khz or 192 Khz, the modulator rate is always 6.1 Mhz.

The modulator is delivering the exact same signal whether the target rate is 44.1, 88.2 or 176.4 Khz (or higher). In light of this, how do the issues you mention with the analogue electronic components affect the different target sample rates differently? If your point was about a difference between 44.1/88.2/176.4 and 48/96/192 I could understand as they have different modulator rates but I do not understand how this would work between say 44.1 Khz and 88.2 Khz.

I also don't see how software algorithms are affected by the speed of the analogue stages? I don't believe they are. Either the software (and the computing hardware it runs on) runs properly or it breaks don't catastrophically. Unlike analogue, there is no graceful degradation of performance. It works or it doesn't. A computer CPU running at 5 Mhz is no more accurate than one running at 3Ghz. The analogue speeds of the components have no bearing on the digital software accuracy. (Of course there are other compromises on the software/digital side but those do not pertain to the points made in the article being discussed as far as I am aware).

The fact that some converters are designed to optimized the frequency response near 20kHz when operating at 44.1 kHz does not mean that there is not some trade-off involved to the audio quality.
Of course. My comment was specifically about that alleged -3 dB point at 20 Khz (and thus a cumulative loss of 12 dB at 20Khz in the example given) mentioned in the article. That doesn't seem to exist in the real world of modern converters and studio monitor speakers. (At least the ones I am aware of). If there are other compromises being made I would be interested in hearing any more information about them but I don't think it helps the cause against ever higher sampling rates to present arguments that do not apply in the real world of modern converters.

Dan Lavry’s response regarding the frequency response of DA converters:
“I agree that many IC makers try and push the response to be very flat at 20KHz, and that is also an issue for quality audio. Trying to pass 20KHz to a very flat .1dB while rejecting 22.05KHz is very demanding for the digital filter (for both AD and DA). A couple of KHz transition from passing to total rejection of audio has the potential to cause problems. By contrast; with a 96Khz sample rate, the transition is around an order of magnitude lower.”
I'm not sure what "very demanding" means technically. To me the only question is: Are the designs achieving what they set out to achieve or not? Based on what I know it seems that they do.

I fully understand what you are saying in theory but it seems that in practise, according to any of the more extensive listening experiments I have taken part in or read about, with good converters people can't actually distinguish between a 44.1 Khz ADC -> DAC loop and a straight wire. In light of that, how serious are these audio problems? Isn't, if not 44.1 Khz, at least 48 Khz more than sufficient for all our conversion needs[1]?

Also, purely on a technical point, the ADC chips I have checked use the same filter slope for 44.1/48 Khz, 88.2/96 Khz and 176.4/192 Khz. [2] I don't mean the same cut-off point in absolute values but the same cut-off point as a fraction of FS. Of course if FS is doubled (or quadrupled) any issues with filtering would be moved even further outside the audible band. I am just trying to figure out what you mean by "very demanding". Surely if there was any overt technical issues with the filter slope/processing load on the systems (like overheating or such), the chip designers would have relaxed the filters slopes at higher rates. Or am I missing something?

Also, again purely on a technical point, it seems the flagship chips I have checked have a transition band on their filters of around 4 to 5 Khz (for 44.1 Khz operation). This means there will be a bit of aliasing of frequencies between 22,05 Khz and whatever the stop-band is (up to 25.6 Khz on the Cirrus Logic CS5381 which was the highest of the chips I checked). Do you see this as a problem or would you consider it a good compromise?

Thanks in advance,


[1] With the obvious exceptions of things like recordings for scientific purposes or recordings intended for, for instance, pitch shifting or other such processing for sound design purposes.

[2] With the exception of the Wolfson WM8786 chip which uses a different filter slope for quad rate conversion. (But the same at single and double rate speeds).