Lavry Engineering Paper on Hi-Res

[Lavry tech]

In response to some of the statements in Jud’s most recent post, Dan Lavry has asked me to publish his response:

 

Dan Lavry’s Response-

The Sampling Theory paper does NOT suggest that there is any “permanent” bit depth limitation or any sample rate limitations. When I wrote the paper, I used the present day technology (8 bits at 100MHz or 16 bits at 1MHz) as a tool to point out that as the speed increases, the accuracy (thus the bit depth) decreases. Years ago, getting 8 bits at 1MHz was beyond the state of the art technology. It would be ridiculous for me to assume that we will (or will not) have 8 bits technology of say 1GHz or 10GHz at some future time… However, at any given time, when one looks at conversion speed and accuracy, one finds that the slower the conversion, the more accurate it is. That was true 40 years ago when I was a young design engineer, and it will be true for as long as the basic principles that govern analog design hold true.

 

The point is that to do an optimal job, one cannot sample too slowly (you need to cover the audio bandwidth in the case of sound), and you cannot sample too fast (you lose accuracy). No one suggests sampling audio at 1Hz. No one suggests sampling audio at 1GHz. So there is an optimal rate! But where is it? First we need to accept the fact that there is some optimal rate. Those that advocated faster is automatically better are not even accepting that fact! Optimal rate depends on the application. Video calls for more bandwidth so we must sample faster. But video conversion is less accurate. Audio needs to accommodate the ear, which does not need video speeds yet is more sensitive in terms of accuracy. The ear does not hear 80kHz; thus sampling too fast reduces accuracy while gaining nothing for it. Think of a camera that can include invisible light at a cost of degradation to the visible spectrum.

 

If one desires to confirm this relationship, feel free to go to the website of any manufacturer that make a wide array of conversion products (such as Analog Devices, TI and more). Check the selection guides of today; check the data from 10, 20, or 30 years ago…. You will see that speed always costs accuracy and accurate conversion demands slower speeds.

 

Again, my example about 8 bits at 100 MHz and 16 bits at 1MHz were there to show the RELATIVE accuracy as it relates to speed. I never stated that a permanent bit depth limit exists; I used (then) contemporary data to demonstrate a point- that speed compromises accuracy and increased accuracy demands lower speed. Technology improves over time, and still, faster will remain a tradeoff against accuracy, as it always has been.

 

Analog designers will understand that statement very well. Say one wishes to “take a sample” and to do so, you need to charge a capacitor. The charging curve is an exponential one – the longer you wait, the closer you get to the actual value of the sampled input. If one reduces the capacitance to speed thing up, you pay a price!

1. A smaller capacitor does not hold the charge as well. It will partially discharge before the AD conversion can complete, resulting in a lower sample value.

2. A larger capacitor reduces switching transients. Switching transient introduce other inaccuracies.

3. And relatively small capacitors (such as found in sigma delta switch capacitor networks) generate more noise; which is the major limitation of that technology today.

 

No analog designer can dispute that!

 

Another example is an OP-AMP. Converters use OP-AMPS that operate at very high speeds, to handle the required fast voltage (or current) “steps”. One can look at settling time of such circuits, and again, the longer you wait after the voltage step occurs, the closer the output of the OP-AMP is to the ideal final value (thus more accurate). The vocabulary is “settling time” (such as settling time to reach less than 1% error). If you “look” at the OP-AMP’s output voltage too soon after the step occurs, the result of the conversion is less accurate.

 

There are numerous other examples of the tradeoffs, all based on basic electrical principles of physics. This is not the place to lecture about analog design. I was probably too detailed as is.

 

So the assertion that I said there is a "permanent bit depth limit” is not true.

Dan Lavry

 

End of response

 

We do appreciate the idea that Dan Lavry is cited as an authority on digital audio conversion; however we would ask that he not be miss-quoted by any means; including taking parts of his paper out of context or making claims that he “says” something in words other than his own.

 

The point is not that conversion at sample frequencies higher than 96kHz is “not accurate enough for audio;” it is that conversion at sample frequencies higher than 96kHz will always be less accurate than conversion at 96 kHz (or lower) with the same technology. As with many other things,there is a point of diminishing return; and thus there is an upper limit for sample frequency to achieve the most accurate conversion of audio.

 

Brad Johnson

Lavry Engineering Technical Support

 

 

[Lavry tech]

Regarding:

“One of [Lavry's] basic points, near the beginning, is that you don't get anywhere near a 24-bit word length due to inherent inaccuracies until you have a sample rate as low as 50-60 Hz.

 

But several people here are totally ignoring this and talking about 24/192.

 

So do you think he is just plain wrong on this?”

 

There is accurate information and inaccurate information. One can produce 24 bits of information using any number of means; the paper was addressing the issue of accuracy. Yes, it is possible to get good results recording audio at 192kHz; but if it were possible to use the exact same converter in a way that it was optimized for 96kHz operation; it would yield more accurate audio information. Part of the problem with making comparisons between recording made at 192 and 96 kHz is that an AD converter that is optimized to operate at 192 kHz will by definition have compromised operation when set to 96 kHz output. All contemporary multi bit AD converters actually sample at frequencies much higher than the output frequency; which is independent of the output sample frequency setting in cases such as 192 versus 96 versus 48 kHz.

 

Regarding:

“The point is not that conversion at sample frequencies higher than 96kHz is “not accurate enough for audio;” it is that conversion at sample frequencies higher than 96kHz will always be less accurate than conversion at 96 kHz (or lower) with the same technology.

This applies only to multi-bit PCM….”

 

No, it does not.

 

First of all, the term “multi-bit PCM” is confusing as it refers to AD converter architecture (multi-bit as versus single-bit) which BOTH utilize sigma-delta conversion and “PCM” which is an output format and can be produced from non sigma-delta as well as sigma-delta AD converters.

 

And, YES, there is a trade-off even with one-bit sigma delta between bandwidth and accuracy in the audio band. It is interesting that so many people think that a system that has extremely high noise energy just beyond 20 kHz requiring it to be limited to a bandwidth of ~20kHz has “more accuracy” because of the very high sampling frequency than a 96kHz multi bit system with a bandwidth TWICE that of DSD.

 

For those interested in his opinion on DSD, there are a number of Posts on the Lavry Forum regarding this matter. Here are two examples:

 

http://www.lavryengineering.com/lavry_forum/viewtopic.php?f=1&t=916&hilit=DSD

http://www.lavryengineering.com/lavry_forum/viewtopic.php?f=1&t=610&hilit=DSD

 

Dan Lavry has spent hours in this and other forums responding to individuals who make assertions without any solid scientific basis. He did feel that he would like to make one final response:

 

Dan Lavry’s response:

You seem to have dismissed what I said about the speed–accuracy tradeoff altogether, and you counter it with what? That 24MHZ one bit is “good”?

 

Sigma delta, as well as most modern multi bit converters, does utilize very high speed at the front end circuitry. So why not claim that “PCM” has a sample frequency of 24MHz? Because it does not represent the audio sample rate. It is the modulator rate! Conversion is much more than how fast one clocks a modulator.

 

The concepts of DSD and multi bit sigma delta are both based on noise shaping. With a given technology (the basic parameters are modulator clock speed which you are confusing with converter sample rate, number of modulator bits and loop filter order), one can have a much better result when aiming at the frequency band that the ear hears. When you accommodate say 90kHz of usable signal range, you get a lot of range that is not usable by the human ear, and for that you pay a price. It is better to accommodate the usable range.

 

You can take the same basic resources (modulator clock speed, modulator bits and filter order) and design a converter for some industrial use requiring 1MHz usable signal bandwidth. It will not have anywhere near the accuracy of a converter aimed at 50kHz usable signal range.

 

Here is an analogy: A worker can dig 10 cubic feet of sand (this will represents some given technology). You can tell the worker to dig a 10 foot long 1 foot wide trench with a 1 foot depth. Or you can choose to dig a 10 foot deep hole with a 1 square foot area. You have to decide what to do. Deeper is better (audio quality) but the application requires some minimum area (cover the audible range).

 

So here I have shown you how higher speed (more signal bandwidth) costs accuracy right up-front, at the block diagram stage of design. That is BEFORE I even touch on the real limitations of the analog tradeoffs between speed and accuracy, including the sample and hold and OP-AMP examples in my previous response.

 

I don’t see why it is so difficult to grasp the concept of the existence of tradeoff between speed and accuracy. I can think of many real-life “cases” where such a tradeoff exists. However, I am not making universal statements about life in general. I am restricting my comments to what I know as a professional with 4 decades of hands-on design experience.

 

Anyone saying that there is no compromise between speed and accuracy does not know electronic circuits. Diverting the conversation into other aspects to avoid reality issues of the most fundamental level is a disservice to those seeking the truth. I have encountered too much stuff like that already in discussions on the internet. Some talked about the advantage of a narrow impulse, ignoring (or being ignorant) of the fact that impulse width is THE SAME THING as signal bandwidth. Others talked about “more samples is better” failing to understand a basic theorem (not a theory, theorem is PROVEN) called the Nyquist Theorem; one of the most fundamental corner stones of technology and engineering. Others claimed that the ear hears way up there, into the range of 100kHz…

 

In Ignoring vs. Paying Attention

“…Since SACDs and DSD files seem to exist; many people who have an interest in good audio seem to like them; and knowledgeable programmers/designers don't seem to have any conceptual problem with how SACD/DSD recordings work; then my conclusion is Lavry's eight references to problems with "accuracy" are hogwash…”

 

I wrote my paper Sampling Theory to dispel the “baloney.” I tried my best to keep it simple, and know it is not easy reading for a novice. I feel that I have done my part, and I cannot reply to every comment on the web, especially when so much of it is based on misinformation. And I do not appreciate labeling the knowledge I have chosen to share with others, which was gained from my 40 plus years of work and experience, as “hogwash.”

 

End of response.