the Basics of Digital and Analog Audio

[gregorio]

This is a simulation of real-world events,

No it is not, the Nyquist/Shannon theorem explicitly states that at least double the sample rate is required for a given bandwidth. There are no cases in audio production where your “simulation” represents the real world of audio recording!

where there are frequencies higher than 20kHz in real sounds, while it is generally believed that the human ear can only distinguish sine waves below 20kHz.

There can be frequencies higher than 20kHz in SOME real sounds but they are virtually always of a low magnitude and it’s irrelevant anyway, the band above 20kHz is deliberately discarded, it has nothing to do with the Shannon Sampling Theorem, it’s discarded because “it is generally believed” the human ear cannot distinguish sound above 20kHz because there is a great deal of robust reliable evidence going back for 130 years or so which demonstrates we can’t and none whatsoever that demonstrates we can!

I use this example to illustrate that the Shannon theorem cannot explain why sounds with frequencies above 20kHz can still interfere with human perception, and why a sampling rate higher than 40kHz is meaningful.

Sure, the Shannon theorem also cannot explain why I can’t see Santa Claus but then in both cases it is not trying to! Again, there is no reliable evidence we can hear sound above 20kHz or that it somehow “interferes with human perception”, there is however robust evidence that it doesn’t even register in the auditory cortex, let alone can be heard! The Nyquist/Shannon Theorem proves there is no loss of information (within a given bandwidth), it does not address human perception or what you falsely believe about human perception.

G

 

[castleofargh]

This is a simulation of real-world events, where there are frequencies higher than 20kHz in real sounds, while it is generally believed that the human ear can only distinguish sine waves below 20kHz. I use this example to illustrate that the Shannon theorem cannot explain why sounds with frequencies above 20kHz can still interfere with human perception, and why a sampling rate higher than 40kHz is meaningful.

False argument, false example.

First, that scenario doesn't say anything at all about our ability to hear above 20kHz. Not a thing.

Second, you either want the 30kHz tone recorded, so you sample at least at twice that rate, like the theorem tells you to. Or you don't want 30kHz, and you filter it out when sampling. Those are the 2 real-world events that we will encounter when recording with any ADC or down converting a file. You instead created a flawed and not real world third situation where you don't filter out the 30kHz, yet sample at less than twice its frequency anyway. All that demonstrates is how doing it wrong is wrong.

Is this going to be sunjam all over again, with illegal signals as justification for legal ones?

 

[TYATYA]

Your OP is NOT the “Basics of digital audio and analog audio”, it’s actually the “Basics of digital and analogue audio Marketing”.

Right!
Marketing words as like this: give me more points, I can redraw a circle precisely than you can do.
All students in school today say: No! I just need 3 points!!!

 

[Roseval]

You mean you are so much down in knowledge that human body is happy with 20khz bandwidth?

Wonder what this arbitrary number is about.
Might it be you mixing up the specs of the red book standard and Shannon/Nyquist?

 

[bigshot]

40kHz is just one octave above 20kHz. It doesn’t represent a lot of sound… and none of that is audible anyway. Super audible frequencies have never been found to improve the perceived quality of recorded music.

 

[old tech]

I'll delete that controversial part.

It is plain BS and therefore not controversial to anyone with a modicum of sound science knowledge.

A format to have a theoretical "infinite information and bandwidth' it would by definition also have an infinite dynamic range and SNR - 1. So far from infinite information, there isn't an analogue format that even matches, let alone exceed CD on these measures.

You also make the point of missing information in discrete sampling. While that is strictly incorrect anyway, what you fail to mention is that there is more missing information with analogue formats, particularly when it involves changes in state of energy (eg electromagnetic to mechanical - you know, the first law of thermodynamics) which is a measurable difference compared to digital formats - heck that is why we digitise analogue signals in all fields and not just audio).

Lastly, while DSD does measure better than CD for fidelity, it is not noticeable to human ears as the frequency response and dynamic range of CD is already at the limit of human hearing. Despite over 30 years of arguments and blind testing there is no convincing evidence otherwise.

 

[OmgBatman]

I saw you getting a lot of hate in the first number of replies, and I'll let you know I thank you for the informative post - thank you.

 

[bigshot]

It really isn’t a controversy and the replies aren’t really hate. It’s just that the OP started out with some pretty basic fundamental misconceptions.

I think if you’re going to write a post in a FAQ format for the science forum, you might want to brush up on the science of digital and analog audio first. If you aren’t knowledgeable enough in the subject to pull off a FAQ, it might be best to take it point by point and ask for input and help to assemble one.

Nyquist is the fundamental principle behind digital audio. It’s probably a good idea to at least understand that before posting diagrams and explanations.

 

[Sha1rholder]

It really isn’t a controversy and the replies aren’t really hate. It’s just that the OP started out with some pretty basic fundamental misconceptions.

I think if you’re going to write a post in a FAQ format for the science forum, you might want to brush up on the science of digital and analog audio first. If you aren’t knowledgeable enough in the subject to pull off a FAQ, it might be best to take it point by point and ask for input and help to assemble one.

Nyquist is the fundamental principle behind digital audio. It’s probably a good idea to at least understand that before posting diagrams and explanations.

Do not disguise your prejudices and shallow understanding of sound as "science" and take pride in it. When someone tells you something beyond your knowledge scope, try to use logic to understand it. Based on a full understanding of Shannon's theory, I can tell you that sounds above 20kHz, once filtered, do not match the original waveform. The essence of Fourier decomposition, which is the basis of Shannon's theory, is to trade accuracy in the frequency domain for accuracy in the time domain, converting between time and frequency domains. "The human ear cannot distinguish sounds above 20kHz" refers to a 20kHz sine wave, but numerous studies have long told us that it is entirely possible that more accurately recorded sounds above 20kHz can indeed affect the human ear in the complex real-world audio environment. This is why Hi-Res and DSD exist. I have demonstrated this with code: the human ear is a physical motion sensor, not a 40kHz (twice 20kHz) sampler. Your doubts about me precisely show that you do not understand the essence of the Nyquist sampling theorem and the Fourier transform. The only thing I learned from you is "Never argue with stupid people," so I did not reply to your previous comments, but now I can no longer tolerate your half-baked arrogance.

 

[bigshot]

Do not disguise your prejudices and shallow understanding of sound as "science" and take pride in it. When someone tells you something beyond your knowledge scope, try to use logic to understand it. Based on a full understanding of Shannon's theory, I can tell you that sounds above 20kHz, once filtered, do not match the original waveform.

Once filtered there are NO sounds above 20kHz on a CD. Humans can’t hear above 20kHz. Frequencies above 20kHz contribute nothing to perceived sound quality of recorded music. Frequencies above 20kHz flat out don’t matter unless you’re a bat or a dog.

I’m not going to call you stupid. You are misinformed by commercial interests looking to sell you something.

All that matters for the purposes of home audio is what your ears can hear. The only way you need to hear it is by means of music reaching your ears and your ears hearing it. That is the same for geniuses as it is for idiots.

 

[Davesrose]

Based on a full understanding of Shannon's theory, I can tell you that sounds above 20kHz, once filtered, do not match the original waveform.

You previously posted that you prefered DSD, claiming it sounded more natural for old classical tape masters. If there was such a thing as infinite accuracy for all bandwidths, so what? The only thing high res would be doing for an analogue source is capturing the distortion that's inaudible (tape masters didn't record relevant high res audio waves). Pro grade tape got close to having a flat response to 20kHz (going to 22kHz).

Frequency Response Charts – What Do They Mean???

 

[sander99]

Do not disguise your prejudices and shallow understanding of sound as "science" and take pride in it. When someone tells you something beyond your knowledge scope, try to use logic to understand it.

Why don't you do that then? You demonstrated that you don't understand the sampling theorem by showing that sampling a 30 Hz signal with 48 Hz sample rate doesn't work. Of course that doesn't work, the sampling theorem posts conditions that you did not meet! You first have to low-pass filter the signal to remove any content >= 24 Hz before it is allowed to sample it at 48 kHz. This has been explained to you already, so why don't you use logic to understand it?

the human ear is a physical motion sensor

The inner ear contains sensor hairs that are tuned to small frequency bands and effectively works as a kind of fourier transformer. None of those sensor hairs responds to frequencies above 20 kHz. If a wave form consisting of for example a 10 kHz sine wave plus a 30 kHz sine wave plus a 90 kHz sine wave enters the inner ear only the hairs that are tuned to around 10 kHz react. Hence you won't hear a difference between that wave form and a pure 10 kHz sine wave.

but numerous studies have long told us that it is entirely possible that more accurately recorded sounds above 20kHz can indeed affect the human ear in the complex real-world audio environment

There have been no studies showing that it can be heard, on the contrary.

This is why Hi-Res and DSD exist.

No, they exist to make money of misinformed customers. (And higher bit depths and sampling rates can be usefull on the production side in the studio, but not as a distribution format.)

 

[Sha1rholder]

You previously posted that you prefered DSD, claiming it sounded more natural for old classical tape masters. If there was such a thing as infinite accuracy for all bandwidths, so what? The only thing high res would be doing for an analogue source is capturing the distortion that's inaudible (tape masters didn't record relevant high res audio waves). Pro grade tape got close to having a flat response to 20kHz (going to 22kHz).

Frequency Response Charts – What Do They Mean???

1. I did not "prefer" DSD. What I was trying to say is DSD usually performs better when reproducing original waveform than PCM. 2. I did not say it sounds more "natural" for old classical tape masters.

 

[Davesrose]

1. I did not "prefer" DSD. What I was trying to say is DSD usually performs better when reproducing original waveform than PCM. 2. I did not say it sounds more "natural" for old classical tape masters.

Sorry that I mistook you for another poster in another thread that was posting similar misconceptions about “Theoretically, it [analogue] has infinite information and bandwidth.” and that DSD is then best at capturing this “perfect” analogue waveform. It’s easy to see why I confused the both of you. My post remains about the limitations of analogue recording (not “controversial” as you posted in defense for removing that sentence). Since the analogue stage, as well as human hearing, are not capable of picking up ultrasonic frequencies, there’s no sense coming up with a digital system that would have infinite accuracy (never mind the waste of file size).

 

[bigshot]

Inaudible is inaudible.