Subharmonics of ultra high frequency information...

[Ethan Winer]

That is not true as a matter of math Jack . As long as we have twice as many samples as we have bandwidth, we can fully represent the signal. More samples are redundant and don't contribute to proper reconstruction.

Thank you for busting that oft-repeated myth Amir. Since that myth has been debunked almost daily in the various forums I visit, I don't understand why people keep repeating it.

--Ethan

 

[JackD201]

I defer to your expertise Amir. I'm looking at it theoretically from capture and reconstruction. On the face of it more samples between null to null would appear to allow less intensive math for the decoding mechanisms. Less blanks to fill so to speak. I'm thinking the benefits are not just in pushing foldback up and out of hearing range as you correctly say. Again theoretically, couldn't reconstruction be designed to take advantage of the added samples in conjunction with bit depth rather than treat them as redundancies as is the case now? I mean the added samples are values between null and peak so can't these be used to determine the slope of the amplitude for the analog section to recreate if not the frequency itself instead of an interpolated value?

 

[JackD201]

Thank you for busting that oft-repeated myth Amir. Since that myth has been debunked almost daily in the various forums I visit, I don't understand why people keep repeating it.

--Ethan

As usual, you take only what suits you and ignore the second paragraph that answers your own question.

 

[FrantzM]

Hi

Question, let's suppose two signals :
f1 and f2.
Both have the same amplitude
Both are of the same fundamental frequency at 11.5 KHz
f1 is a pure sine wave
f2 is a sawtooth signal or a square wave...

Do they sound the same under controlled conditions?

I don't truly know the answer to this question .. I do however would think that they wouldn't sound the same...

If they don;t then the higher sampling frequency may have to do with their sounding different wouldn't you think?

 

[amirm]

Jack, if I had not sat through the proof of Nyquist in my college course, I would not believe it either. It seems totally non-intuitive that you so few samples let you reconstruct a continuous waveform. Further, no interpolation actually occurs between those values. The waveform is generated perfectly with no guess work.

The key to understanding it is that the theory applies to bandwidth limited signal. If you filter out everything above 20KHz, then the waveform has no choice but to follow the path of those few samples if that makes sense. In other words, those two samples provide the only path the signal could travel.

Imagine if I had a road where I could only have a left or right turn every half a mile. To give you directions then, if I gave you points along the way that where half a mile apart, then it would be just as good as if I gave you directions that had quarter of a mile distance. Giving you more points doesn't help accuracy. Same is true of sampling signals. If you pre-filter to make sure you have nothing > 20 KHz (equiv. of me saying no turns at less than half a mile), then you only need 40,000 points to represent that path. Having more doesn't help there any more than it did in the map example I just gave.

 

[amirm]

Hi

Question, let's suppose two signals :
f1 and f2.
Both have the same amplitude
Both are of the same fundamental frequency at 10 KHz
f1 is a pure sine wave
f2 is a sawtooth signal or a square wave...

Do they sound the same under controlled conditions?

I don't truly know the answer to this question .. I do however would think that they wouldn't sound the same...

If they don;t then the higher sampling frequency may have to do with their sounding different wouldn't you think?

Well, we can deconstruct the question to see if we can arrive at the answer:

An idealized Sawtooth signal is made up of its frequency + sum of all of its harmonics going into infinity. In other words, to make a sawtooth, we take the 10 KHz and add small amounts of 20 Khz, 30 KHz, 40 Khz, etc. The sum goes into infinity. Therefore the signal has infinite bandwidth. Same thing occurs for square wave except that we only use the odd multiples (harmonics).

In a digital system, we limit the bandwidth relative to sampling rate. This means that the we chop off everything after 22 KHz for CD. In case of Sawtooth, we now have a completely new waveform that is a simple sum of two sinewaves: 10 KHz and 20 Khz. The waveform looks nothing like a sawtooth but it is different than f1 because it has two sinewaves mixed together.

Square wave would lose all of its harmonics because its next component is at 30 KHz and we have chopped that off with the filter. So all we have is the original 10 KHz.

So I would say that the square wave and sine wave would sound the same but sawtooth would sound different on CD.

If we increase the sampling rate, we get to preserve the higher frequencies. At 88 KHz, we would have more of the harmonics preserved and the three waveforms now look very different on the scope. To hear the difference though, requires answering the question posed in this thread .

 

[tony ky ma]

Why have to filter out those ultra sound range frequencies in both end ? ( in digital I don't know) whatever signals that microphone can pick up should be in the air when reproduce no matter it is can be audible or not
tony ma

 

[amirm]

No, just the higher frequencies. You can as low as you like.

 

[tony ky ma]

I did hear they don't sound the same from the speaker of different wave forms in audible frequency ( sig-gen to amp to speaker)

 

[FrantzM]

Amirm

Back in my college days, I also had to demonstrate the Nyquist Theorem and it almost bothered to admit it was correct and that once asignal is indeed sampled at at least twice the highest frequency in the signal it can be perfectly recovered.. The fixation we all have on the imagery of the "chopeed" sinusoiidal , somewhat makes this theorem non-intuuitve ...
Vut, that wasn't what I was addressing. I should have made it clearer:

The question is given the two signal I mentioned earlier, can we reliably distinguish between a pure tone (the sinusoidal) and another NOT sinusoidal but of the sam amplitude and frequency?
In Other words does a sinus sound to us like any other signal? once we pass a certain frequency? say 11 KHz?
Everything else being equal... No change of equipment, controlled environment

 

[DonH50]

A few comments to supplement Amir's excellent posts:

1. Nyquist has to do with information bandwidth and, in the case of audio, the highest frequency content of a waveform. So, as Amir states, we need more bandwidth and thus a higher sampling rate to reproduce a signal that has more than a single tone at the fundamental frequency. Sawtooth, square, etc. signals require more bandwidth than single-tone sine waves at the same fundamental frequency. (Amir, in your post you should say one must filter signals >= 20 kHz for a 40 ksps system -- a signal exactly at 20 kHz gos to d.c. Yes, I know you know that!)

2. While the arguments rage eternal, most of the testing I recall says harmonics in the signal above your range of hearing do not add to the sound. In that sense, if your hearing falls off over 10 kHz, then a 10 kHz sine and square wave would sound the same. That does not include the impact of nonlinear mixing that may occur in the electronics or in your ears, however.

3. Tony, the digital system cannot accurately capture and reproduce signals above the Nyquist limit, that is 1/2 the sampling frequency. Frequencies over that, if not filtered, will appear down in the audio band based upon their relationship between the signal and clock frequencies. This can make for bad sound and is one reason higher frequencies must be filtered before the ADC sees them. It's a digital thing...

4. Having a higher sampling rate does in theory make it easier to reconstruct signals when non-ideal filters are considered. That is, non brick-wall filters. However, higher rates mean wider noise bandwidth (and thus more noise), can lead to more ringing and other artifacts, make power supply design and filtering more difficult, and make it harder to realize highly-linear (low-distortion) analog circuits in the signal chain. Speaking as a designer, I want no more bandwidth than required.

5. A digital system can produce a d.c. output; a phono cartridge or tape head cannot. This probably matters to nobody, just thought I'd mention it. The phono cartridge and tape head can produce much higher frequencies than 20 kHz, where a CD must filter those frequencies out, of course. Same comment.

 

[FrantzM]

Don

As I have mentioned earlier, I don't know the answer but am not sure ALL 11 KHz tones of equal amplitude sound the same. if they do , fine all bets are off and Redbook CD is all we need, if they don't , it seems to me a case where capturing and reproducing frequencies above 20 KHz could have some advantages. Now I am not sure I understand the "non linear mixing that goes in the ear", the ear wil react to a tone in a way the brain interprets as a perception, whether the perceptions are the same for ANY 10 KHz signal is exactly what I am wondering about... not the mechanisms by which they are perceived , if indeed they are.
If I were to take part 5 of your argument

A digital system can produce a d.c. output; a phono cartridge or tape head cannot. This probably matters to nobody, just thought I'd mention it. The phono cartridge and tape head can produce much higher frequencies than 20 kHz, where a CD must filter those frequencies out, of course. Same comment.

then 24/96 is interesting (emphasis on the 96 KHz here rather than the 24) since it reproduces flat from DC to 48 KHz.... Now in term of bandwidth 100 KHz is IMO piece of cake and would not provide much problem in term of circuitry filtering, shielding, etc .. one can cope with the caveats, if indeed it provides benefits in term of information retrieval.

 

[DonH50]

Me neither, Frantz. I believe Kal has discussed nonlinear mixing in the ear/brain system; it's not something I am competent to discuss (which doesn't stop me, natch ). As I said, though an "ultrasonic doubter" myself, I have read studies that go both ways.

Of course, since my hearing now cuts off between 10 and 12 kHz, I am pretty sure they would sound the same to me...

 

[Kal Rubinson]

Of course, since my hearing now cuts off between 10 and 12 kHz, I am pretty sure they would sound the same to me...

Well, look at it this way: CD now offers you an octave more bandwidth than you need.

 

[DonH50]

LOL! Had not thought of that; you are mucho gracious, Kal! - Don

 

[Ethan Winer]

As usual, you take only what suits you and ignore the second paragraph that answers your own question.

I have no idea what you're talking about. The notion that digital audio is missing information or "detail" or "resolution" between the samples is flat out wrong. I see it repeated then debunked all the time. That's all I was commenting on. I honestly don't understand why people who clearly need to learn stuff are so hateful toward those who are just trying to help.

Edit: Reading my earlier post again I can see what you might have felt attacked, but that was not my intent. I honestly don't know why this myth is still so prevalent. Not unrelated, a few months ago Consumer Reports magazine published a landmark article showing that not only are vitamins not necessary for most people, but they can actually be harmful and increase the risk of cancer in some cases. I bet a year from now vitamin sales will be the same as they are today, or maybe even more.

--Ethan

 

[Phelonious Ponk]

I honestly don't know why this myth is still so prevalent.

It's all a part of an on-going effort to show evidence of the superiority of choices that have no evidence of superiority.

Tim

 

[JackD201]

No skin off my back Ethan even if you meant it.

I did ask Amir who is clearly one of great experience in this field to write an article to help me and hopefully others understand the relationship of bit depth and sampling rates as that seems to be where my error lay. Do note that Amir did qualify that I was wrong mathematically which I quickly accepted because he is absolutely correct in those terms. I asked that he write the article, because especially during capture (ADC) I would like to understand how the peaks and troughs are timed with the sampling frequency. Given perfect clock performance with sampling occurring in perfect intervals what happens when the incoming electrical signal's peak or trough does not fall in the sample window? With insufficient sampling rates we know it will result in aliasing. In practice and not math however, and I ask this as a legitimate question and not a challenge, is Nyquist sufficient to capture the combined tones and more specifically how does the added bit depth of hi-res or even redbook vs compressed affect the gradations of output voltage not just above the actual and not theoretical noisefloor or above the usable additional dynamic range. We're introducing a new time variable, one that I DO NOT KNOW is considered by the theorem or not, where, theoretically, higher sampling rates increases the probabilities of more accurate data capture of an incoming analog signal which would again theoretically increase resolution particularly in low level information in a mixed signal.

 

[DonH50]

There is a thread about sampling in the tech talk forum that might help. I tried to minimize equations, but it's hard to get rid of them all, sorry!

http://www.whatsbestforum.com/showthread.php?1209-Sampling-101

 

[JackD201]

Interesting. This may make for the first Digital vs Digital debate in WBF history.