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Digital to Analog with 100% accuracy

erikveach

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Certainly...but if you PREFER the analog sound, what would you need to do in your digital system to mimic it? I make the case that there is basically "sampling noise" in analog sound based on the physical properties of the medium used. Then it's simply a matter of determining what effective sampling depth and rate is produced by the medium.
 

erikveach

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That was your first mistake.
When small enough you can use step and point pretty much interchangeably with very little difference in the mathematical results between them. Where is the mistake? All modern approximations using calculus utilize this same approximation method.
 

NTK

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When small enough you can use step and point pretty much interchangeably with very little difference in the mathematical results between them. Where is the mistake? All modern approximations using calculus utilize this same approximation method.
If your math is good enough, go read Whittaker's paper published >100 years ago.
https://zenodo.org/record/1428702
 

waynel

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When small enough you can use step and point pretty much interchangeably with very little difference in the mathematical results between them. Where is the mistake? All modern approximations using calculus utilize this same approximation method.
You are claiming that LP has 730MHz bandwidth and 104dB SNR (17-bit ) these are both provably and laughably false.
More like 60-70dB SNR and 20KHz BW (depending on cartridge)

https://en.wikipedia.org/wiki/Comparison_of_analog_and_digital_recording
"a theoretical vinyl LP is expected to have a dynamic range of 70 dB,[6] with measurements indicating performance in the 60 to 70 dB range "

"The frequency response for a conventional LP player might be 20 Hz to 20 kHz, ±3 dB. The low frequency response of vinyl records is restricted by rumble noise (described above), as well as the physical and electrical characteristics of the entire pickup arm and transducer assembly. The high frequency response of vinyl depends on the cartridge."
 

erikveach

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If your math is good enough, go read Whittaker's paper published >100 years ago.
https://zenodo.org/record/1428702
Good to know...thanks for sharing. Seems a bit tangential to what I'm proposing though. Feels like a general discussion of recreating functions through a series equation: Fourier, etc. My discussion is more about how physical properties mimic digital properties in some respects and so that could be used as a basis for creating an "equivalency" between sources, for those who are interested.
 

erikveach

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You are claiming that LP has 730MHz bandwidth and 104dB SNR (17-bit ) these are both provably and laughably false.
More like 60-70dB SNR and 20KHz BW (depending on cartridge)

https://en.wikipedia.org/wiki/Comparison_of_analog_and_digital_recording
"a theoretical vinyl LP is expected to have a dynamic range of 70 dB,[6] with measurements indicating performance in the 60 to 70 dB range "

"The frequency response for a conventional LP player might be 20 Hz to 20 kHz, ±3 dB. The low frequency response of vinyl records is restricted by rumble noise (described above), as well as the physical and electrical characteristics of the entire pickup arm and transducer assembly. The high frequency response of vinyl depends on the cartridge."
Certainly in practice that's true. I mention in the article that the mathematics are a essentially an oversimplification for purposes of generating a theoretical target.
 

erikveach

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Thanks for all your comments. It's great to generate discussion. I appreciate it.
 

solderdude

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Digital sound, on the other hand, is made up of a series of discrete steps in its audio signal that change quickly enough that they give the illusion of a continuous signal when fed to a speaker. This is very similar to the way a video is made from a series of still images that are cycled through fast enough to give the illusion of smooth motion (hence the original phrase “motion pictures”).

It starts out with the biggest nonsense of all. Aside from some filterless NOS DACs playing 44.1kHz files can you show the steps to exist in reality ?

You could say that since a digital discrete signal is merely an approximation of the actual sound

No.. it is a VERY, VERY close approximation to the signal that was coming from the master but in almost all cases that master was digital but in a higher bitrate and bit depth.
That approximation is MUCH closer to that original recording than any direct cut vinyl master can ever dream of.

An analog signal is carved directly into the grooves in the record

No, it is carved in a master disc which is used to make a press mold which again is used to press grooves into a blob of vinyl and comes out as a disc with a groove on it (usually one on each side)

Do you really think that vinyl is limited only by the size of vinyl molecules ?
Is the frequency range of vinyl really limited by molecule size ?
Not by physical limits from the lathe, the 'protection' in the cutting mechanism to avoid needles jumping out of grooves, the limitation of the used master, the limitation of the pre-amp ?

digital audio should be able to meet or exceed the performance of analog sound in both technical quality and sound preference.

News flash digital audio far exceeds vinyl and is always 'less' than the original recording (which in most cases is digital recorded and manipulated)

The fact that the changes made to the original recording by the mastering process, the vinyl cutting head of the lathe, the degradation right up to the pressings, the used cartridge (with all its various aspects), the adjustment and arm, the speed variances, the used RIAA pre-amp and still an enjoyable sound is coming from this (despite and thanks to the alterations) can be quite enjoyable to human ears says a lot about how forgiving the brain is dealing with the distorted original signal.

Yes, vinyl can sound more pleasant that doesn't mean it is more accurate or truthful.
 

waynel

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Certainly in practice that's true. I mention in the article that the mathematics are a essentially an oversimplification for purposes of generating a theoretical target.
A theoretical vinyl LP has 70dB SNR. To get to over 100dB SNR even theoretically the LP would have to be made of diamond.
 

Wes

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"That Ol' Six Sigma - it's good enough for me"

- sung to the tune of "That Ol' Time Religion"
 

erikveach

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It starts out with the biggest nonsense of all. Aside from some filterless NOS DACs playing 44.1kHz files can you show the steps to exist in reality ?



No.. it is a VERY, VERY close approximation to the signal that was coming from the master but in almost all cases that master was digital but in a higher bitrate and bit depth.
That approximation is MUCH closer to that original recording than any direct cut vinyl master can ever dream of.



No, it is carved in a master disc which is used to make a press mold which again is used to press grooves into a blob of vinyl and comes out as a disc with a groove on it (usually one on each side)

Do you really think that vinyl is limited only by the size of vinyl molecules ?
Is the frequency range of vinyl really limited by molecule size ?
Not by physical limits from the lathe, the 'protection' in the cutting mechanism to avoid needles jumping out of grooves, the limitation of the used master, the limitation of the pre-amp ?



News flash digital audio far exceeds vinyl and is always 'less' than the original recording (which in most cases is digital recorded and manipulated)

The fact that the changes made to the original recording by the mastering process, the vinyl cutting head of the lathe, the degradation right up to the pressings, the used cartridge (with all its various aspects), the adjustment and arm, the speed variances, the used RIAA pre-amp and still an enjoyable sound is coming from this (despite and thanks to the alterations) can be quite enjoyable to human ears says a lot about how forgiving the brain is dealing with the distorted original signal.

Yes, vinyl can sound more pleasant that doesn't mean it is more accurate or truthful.
I agree with your conclusion wholeheartedly. And certainly "steps" is just a convenient presentation. But, think of the people this article is aimed at. It's an acceptable way to present it that does not convey any patently false information, except at a mathematical detail level that the vast majority reading that article wouldn't understand. What I was trying to accomplish was to show some comparison, from a theoretical standpoint, of how even vinyl has its own physical limitations that in some sense is also trying to mimic a "real" sound in the same way a digital signal is. And therefore you could compare them in an "apples to apples" way from that perspective. I haven't seen anyone else approach it from that perspective yet, so I thought it would be an interesting exercise that might resonate with some readers comparing the two methods. I thought it might be appreciated here and generate some further conversation relevant to that type of comparison style. But perhaps this was the wrong thread to share that idea.
 

voodooless

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Ok guys I get it. I don't need any more comments thank you all.
Nah, your not getting off that easily.. There are as always a fair bit of questions left unanswered because most people just try to answer the question from their own vantage point. Very often that won’t fully help the asker. So:

Is it possible to convert the digital signal to analog signal with 100% accuracy or to reconstruct the an analog signal to its exact true form.
Why do you ask? What is your definition of 100% accuracy? What is your definition of “true form”?
 

solderdude

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But, think of the people this article is aimed at. It's an acceptable way to present it that does not convey any patently false information

The people it is aimed at receive misinformation.

Vinyl has HUGE technical shortcomings compared to digital.
The fact that our hearing still totally accepts the 'alterations' and even prefers it is a totally different matter.
 

mansr

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Certainly in practice that's true. I mention in the article that the mathematics are a essentially an oversimplification for purposes of generating a theoretical target.
You say oversimplification, I say gross misrepresentation.

And certainly "steps" is just a convenient presentation.
Convenient, easily understood, and entirely wrong.

It's an acceptable way to present it that does not convey any patently false information,
Except that it does.
 
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