I asked:
“1) do you base the premise on a Laplace, Fourier, or z-transform, or primarily based on published work by Nyquist? If based on Nyquist's published work, have you also considered Bode plots for similar analysis? Some people believe the Bode approach is more quantitative. If you have derived your theories from the interaction of the Laplace and Fourier transforms, do you resolve their intersection in the s plane or through the poles and zeroes?”
Mr. Lavry replied:
"My paper and the concepts are based on Nyquist theory. I use Laplace, Fourier and z transforms, as well as Bode plots “all the time”, but those math and engineering tools have nothing to do with the basic concept. Sure you can do a bode plot to show gain and phase, or do an FFT and so on. You can use other tools as well. The Nyquist concept stands to whatever you throw at it:
The digitized waveform contained 2 “types of energy”:
A. The signal content below Nyquist is the EXACT signal prior to digitizing (such as the exact audio signal)
B. The signal content above Nyquist is the “error signal” or “difference signal” (difference between original and digitized)
Therefore, filtering (removing) the energy above Nyquist from the digitized wave leave only the energy below Nyquist, thus the original signal. That includes everything (amplitude, phase and all)."
I reply:
Can you envision a circumstance where higher sampling rates might be useful? The reason I ask this is because s, z, and F transforms, as well as Nyquist and Bode are rooted in an impulse-response sampling. Most discussion on these topics is presented as 2-D matrices. The way it is applied to communications implies (for the purpose of this discussion) a reconstruction from a signal in a wire, which originated from some perturbation in a transducer of limited physical response (a 3-D pressure wave creating harmonic vibration on a 2-D medium, a 3-D guitar string inducing current in a magnetic pickup, etc.). If these theories are designed for a signal flow in an already-reduced transmission medium, then can they really apply to a more "real" environment, and maintain relationships between infinite arrays of input, or does the conversion have to be re-designed? If it has to be re-designed, at what point must this occur? Another way of stating this is that the ideal sinc function looks good on a Euclidean 2-D or polar 2-d plot, but does the same apply to a Euclidean 3-D plot, spherical, or cylindrical plot? What strange phenomena would limit its extrapolation into higher dimensions? How and why must we start to "extract" information rather than "sample" it?
I asked:
"2) since the bandwidth is frequency-limited by Nyquist, then so is the space. As we move into more time-domain-related models, such as node interactions between output (even if limited to 20kHz), do you agree that we require higher samples, even if extrapolated?"
Mr. Lavry replied:
"Time domain and frequency domain are ONE IN THE SAME! One may choose (or have reasons) to view or measure in one domain or the other. I talked about it my paper, but it is really a fundamental concept. What happens when you try to pass a 1usec impulse through say a 20KHz bandwidth? The 1usec impulse contains energy at frequencies way above 20KHz. What happens when you remove (filter) the energy above 20KHz? You are left with a wider impulse, a 20KHz impulse. People that talk about “better time location” because of “narrower impulse” are wrong. The lowest bandwidth in the chain (mic, speaker, the ear or whatever) defines the lowest bandwidth, thus the impulse width.
Also, some people confuse time delay with bandwidth (impulse)."
I reply:
Inverting frequency into time or changing the way the data is handled is not the purpose of my question. What I am trying to ask is that if we look at speaker-speaker interactions, and examine phenomena such as nodal lines and antinodal lines resulting from a two-output source (not even considering that these sources are nonideal), we are starting to degrade the signal and apply limitations on how the speakers can produce sound. This is apparent in a pair of $5 speakers, and it is apparent in $500,000 speaker arrays. So at some point a better speaker design may come about...perhaps in the year 2050...which is not limited to the original constraints of traditional speakers. Such a speaker might entail, perhaps, billions upon billions of nano-sound devices that completely envelope a room...who knows? But if we have perfect input and output, might there be a need for a different "technique" for conversion, and if so, what do you envision that to be? This discussion is beyond Nyquist as the audio world has been referring to it, and perhaps even beyond "sampling".
I wrote:
3) Though the concept of megapixels on a camera don't correlate directly to sound (though in some ways they do), can you concede that the energy transfer through the camera CCD (i.e. visible light reconstruction) is analogous to the frequency (energy) dependence in sound?
Mr. Lavry replied:
"I am not going to get into video. I only touched on “pixels” because “the more is better” catch phrase was used to promote that 192KHz nonsense. The number of pixels has to do with the PRESENTION of the information. Nyqusit theory is about INFORMATION.
Clearly, if you have few pixels, the picture will look granular, and that is because there is no mechanism to correct for that poor presentation. Neither the display, nor the eye can compensate or correct for “not enough pixels”. In fact, much of the video display technology is BASED ON keeping the information separate for each pixel. For a given frame, one pixel is bright red; the adjacent one is low brightness green…. I do not consider such a process analogous to one continues analog signal. The display signals are “broken up” by XY coordinates” and possible color…
But in the background, the video signal itself (containing all the video information) does obeys Nyquist.
Audio (or DA process in general) is NOT analogous to video display technology. We do not have to separate the information onto individual pixels and colors, or into 60 frames of 525 lines each second… We do have a mechanism to “fill in” between samples, and the “fill in” is not an approximation. As long as we obey Nyquist, it is a PERFECT “fill in”. What happens between the dots is the exact duplicate of the original signal. If the curve between 2 sample times were concave, the “fill in” will be concave. If it were convex, or a straight line or what not, it will be reproduced that way. NO NEED FOR ADDITIONAL SAMPLES IN BETWEEN! That is what Nyquist is all about! How do you execute that “fill in”? By using a filter to remove all the energy at frequencies above Nyquist. That is all.
Again, the outcome is the original signal. You can look at it any way you please, and it is the exact original signal. Shine a light on it, do a Bode plot, look at the phase… You will not find a difference between the original analog and the reconstructed (AD than DA) waveforms."
I say:
Then let's forget about megapixels. Let's discuss a single CCD pixel, which translates light energy into electronic energy. The CCD pixel is light sensitive, and is reponsive to a bandwidth of photonic energy. The camera lens directs light onto the CCD pixel, and by adjusting the aperture, the amount of light can be controlled to optimize exposure onto the CCD pixel. There is a limit to how far the lens aperture can be closed before lens diffraction onto the CCD renders no further gain in light responsivity and lens properties, and this correlation between aperture and pixel sensitivity is also falls under Nyquist theory. But now take a step back. We are only dealing with one CCD pixel, which is not nearly enough to "image" the space. And even if we use "infinite" megapixels, the space is not truly rendered because it now exists on a 2D CCD array. And the positioning of the CCD pixels to produce a distinguishable image falls under Nyquist theory. Now let's take a step back even further. The picture we have exists *only* in 2D space, so to reconstruct 3D space, we must now develop another technique, such as stereo imaging, triangulation, time-of-flight, and others. The bases for these principles fall under Nyquist principles. And, to take this further, so does the human retina itself.
I hope this string of thought helps to illustrate my principle--that even though a source, input, or output may be limited, there are permutations that don't follow the "rules" that we've been designing for the past several centuries.
I asked:
"4) do you believe it is the job of the audio designer to address these topics? If so, which type of designer should take the lead?"
Mr. Lavry replied:
"Please clarify what you mean by “an audio designer”. In our industry there are both “ear types”, and “technical types”. I do not think the ear types can be expected to lead audio in a technical arena. I have seen occasions where unqualified ear types claim the lead, such as in the case for 192KHz sampling.
I know many dozens of EE (technical types), and the majority do not get into signal theory. Many are into computers, and are too busy with their issue. Most designers of AD and DA converters are pretty weak on the theory side, and are busy buying ready made IC’s solutions, to be “glued” on a printed circuit board, into a fancy chassis and out the door.
But there are those that know the technical issues. You will be amazed at the consensus regarding 192KHz when the issue is discussed privately. People just do not want to take a stand against their companies.
I can afford to be a 192KHz whistle blower, because I own my company. No one will demote me or fire me. Is it my job to take the lead? I am not sure. It would be easier to just glue those IC’s on the boards. Instead, I took weeks and months to PROTEST."
I reply:
By audio designer, I mean an owner or employee of a company such as yours, that creates audio products for mass or niche consumption. How far should the designer of a product drive the market? Should the designer expect the rest of the industry to follow their lead?
I asked:
"5) do you believe the reconstruction phase low-pass filters are becoming good enough for us to overcome the infinite support in the spatial domain?
6) how do you model lead/lag compensation design?
7) how do you calculate the convolution of the sinc function?"
Mr. Lavry replied:
"Let me take a rain check on the last 3… work calls!
BR
Dan Lavry"
I reply:
Thanks for your responses on the first 4. I look forward to the others if you have time.
REGARDING MR. LAVRY'S POST ON TYING A STRING AROUND A SPHERICAL BODY AND MXERYUS'S POST ON "DOUBLE-CHECKING MR. LAVRY'S MATH AND NOT FINDING A SINGLE MATH MISTAKE":
I offer the following anecdote:
1) given: A = B
Now multiply both sides by A to achieve:
2) A*A = A*B
Now subtract B*B from both sides:
3) A*A - B*B = A*B - B*B
Now factor both sides:
4) (A + B) * (A - B) = B * (A - B)
Now divide both sides by (A - B):
5) A + B = B
What happened here?!!!???! The math was "good" but the result was wrong!!??! How can equation (1) be the same as equation (5)?
Another "funny" way of saying this is:
"Using statistics, I can prove that the average human being has exactly one testicle!"
It is important to remember in math that it is a useful tool, but it must be applied to the correct situation. This correct situation in mathematics is often referred to as "assumptions." Hence, my question on the 96kHz sampling rate being the "end all, be all" of sampling relates not to the math, but its application. I see a lot of people throwing 192kHz, 96kHz, etc. numbers around, but really what are we achieving by all of this? I don't believe it's anybody's duty to "prove" that we must not go beyond 96kHz. I DO believe it is all of our duties to get to the realities of the physics, math, anomalies, and even perhaps a bit of intuition to progress the art of audio.
In a previous topic that was grossly derailed, I was asked to "define" what I consider to be the "ideal" sampling rate, and I declined to comment because of the tone that the message board had adopted. Before I make such a comment, I must be sure that we are all on the same page as to what must be achieved. But I can say this: if microphone techniques and speaker techniques suddenly demand different approaches to A/D and D/A, and the devices are not ready because the capable designers decided to "disprove the industry" rather than re-define it, I will feel slightly ripped-off, because our lifetimes are precious.
Sincerely,
My World
