How Science Got Sound Wrong

terry9,   No worries on being confused about this. I find that many audio writers, many people in the audio industry period, and certain many (most) on audio forums do not get this concept. When you do the math (no literally go through the math), which I have not done in years, it becomes quite obvious how it works (after the 3rd of 4th reading).

Let me do a more real world signal. We have a 24 bit audio system, so it captures with a resolution of about 1/16.7 million, though practically will be closer to 1/1-2 million. Let’s say the system is sampling at 100Khz, and the system is bandwidth limited to 20KHz. Now let’s say we have 10KHz signal.

One key concept in a bandwidth limited system is that you cannot have just a pulse 1 waveform long, i.e. you can’t have a 1Khz waveform that last exactly 1 cycle. That would violate the bandwidth of the system because in a bandwidth limited system you cannot start and stop instantly. You can’t start and stop instantly in the real world either.

Here is where it gets harder. So these two signals, both 1KHz tones, separated by 1 microsecond arrived at these two ADCs. Let’s assume that Signal B arrives at Channel 2, 1 microsecond before Signal A arrives at Channel 1. To make the math easy for me, let’s assume that Signal A arrives at exactly 0 phase. Here are the digital outputs for the first 10 samples at 1KH and 20KHz. This is a DC offset AC signal, so the numbers go from 1 to 2^24.

You can easily tell these numbers do not represent the same signal, there is definitely something different about them. Your next question may be about accuracy / resolution. Jitter will obviously impact the inter-channel timing accuracy. I have not looked at the math in a while, but as you approach the SNR, I remember there is an increase in the inter-channel timing uncertainty.

• 1KHZ
  
• Ch1 / Ch2
• 8,388,608 / 8,441,314
• 8,915,333 / 8,967,925
• 9,439,979 / 9,492,249
• 9,960,476 / 10,012,218
• 10,474,769 / 10,525,779
• 10,980,830 / 11,030,906
• 11,476,660 / 11,525,605
• 11,960,303 / 12,007,923
• 12,429,850 / 12,475,958
• 12,883,448 / 12,927,862
  

We can do it at 20Khz as well

• Ch1 / Ch2
• 8,388,608 / 9,439,979
• 16,366,648 / 16,628,630
• 13,319,308 / 12,429,850
• 3,457,907 / 2,646,210
• 410,567 / 798,368
• 8,388,607 / 9,439,979
• 16,366,648 / 16,628,630
• 13,319,308 / 12,429,850
• 3,457,907 / 2,646,210
• 410,567 / 798,368

This is 20KHz, 90db down from full. As you can see, there are still substantial differences between the channels. This is 20-30db above the noise floor of a good ADC.

• Ch1 / Ch2
• 265 / 298
• 281 / 314
• 298 / 331
  
• 314 / 347
• 331 / 362
• 347 / 378
• 362 / 393
• 378 / 407
• 393 / 421
• 407 / 434

terry91,067 posts11-15-2019 12:29amThe nature of the signals is irrelevant. It is the relative timing of the encoding that matters. If the sampling rate is not high enough, or the jitter rate not low enough, then two signals differing by 1 microsecond will be encoded as identical.

Perhaps an example will help you to understand my confusion. It seems to me that if sampling is done at a frequency of 1Hz, and two signals differing by 1 us are detected, they will be encoded in the same pulse about 999,999 times out of 1,000,000. Which logically implies that sampling rate is intrinsic to the issue.

Perhaps you could point out the source of my confusion.

terry9,

Are you familiar with Shannon-Nyquist theorem? I provided the rather long-winded wikipedia article link below.

In a bandwidth limited system, if the sampling rate is 2x the bandwidth, you can capture all the information, including relatively timing information. I.e. with a 100KHz sample rate, you can capture everything in up to a 50Khz bandwidth limited signal. For practical reasons of analog filters, you normally want to sample 4x or more the target analog bandwidth so by 1/2 the sample rate there is no more signal.

Within the realm of signal capture and reconstruction, I would consider this established fact, though many, without the requisite knowledge, do not understand (or at least accept) the premise.
https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem

A system, with a 20Khz bandwidth, can still respond/detect a signal in microseconds. A real world impulse may last only a few microseconds, however, as your ear is bandwidth limited, you won't perceive an impulse as only lasting a few microseconds, you will perceive it lasting 10's of microseconds or longer, just as when you hit a woofer with a short impulse, it does not stop moving at the end of the impulse.  In those respects, you can reconcile both a 20khz bandwidth limited system and microsecond impulse timing.

akgwhiz1 posts11-15-2019 12:32amNew here but I found his points, yes his science, very intriguing. To the point I thought, heck, hes got it right. But I cant help but wonder, even a fully digital stream/source/path ultimately has to be reproduced through a vibrating speaker. It seems that this is a massive integration or smoothing, each connected (albeit complex) peak and trough lasting way longer than the neural timing. Accepting his points, maybe this is digital's way to get by as well as it does. BTW, I'm not picking sides, just the way I stated it.  

Just when I'm sure its all just swirling down the drain along comes glupson with this:

This year is coming to an end.

Is it time to start submitting "Post of the year" nominations?

This has to be one of the strong contenders.

"Do yourself a favor. Skim right past the loser wannabes - above and to follow, as night follows day- and appreciate those like me who thank you for posting this brilliant article."

This is not even a post. This is literature.

Indeed.

Thanks!

I’m afraid that article is the same old song and dance. What is much more interesting are the ideas of Peter Belt and his whole free wheeling approach to sound and how the local environment affects our perception of sound. These ideas help explain why cell phones 📱  in the room degrade the sound, why books in the room degrade the sound, why unused cables and electronics in the room degrade the sound. Even why our hearing is degraded by having clocks  ⏰ or watches in the room. Things of that nature. Mind-Matter Interaction. Mind over matter. Much of the standard bologna of the theory of perception of sound has become trite.