ORIGINAL: Roflcopter

Seriously, cannot say - just went over his other material, and the man sure knows his stuff, however crazy the above may sound:

maybe read this review as well:

http://www.enjoythemusic.com/magazine/viewpoint/0904/aachapter60.htm

An audiphool review with effectively 10 days between listening to the original sound and the new and improved "tube like" sound? Bollocks. Anyone that has any clue about this would do a double blind listening test.

and to stay on-topic:

http://www.mother-of-tone.com/cd.htm

scroll to the bottom, the last bit is interesting.

Sorry but that is just more bollocks. He mentions the reconstruction filter but keeps showing graphs of the digital data before reconstruction. In my opinion, the guy doesn't really understand what he is talking about.

He seems to be a snake oil merchant catering to the audiophool market.

UnderTow

Well one concept that might help to understand this idea a tiny little bit better: You only need two points to perfectly define a circle. Adding any more points to the circle won't tell you anything extra about the circle. Now if you know that a sine wave is just a circle drawn out over time... you are half way there. :) Maybe this animation will help to visualize this:http://www.rkm.com.au/ANIMATIONS/animation-sine-wave.html

As far as summing is concerned, remember that in a DAW that is sample accurate (and has proper automatic plugin delay compensation) all the samples on all the channels that you are summing are at exactly the same spot in time so when you add two sample values, timing (aka the number of sample per second aka sample rate) is irrelevant. What is important is the accuracy of each sample value. The accuracy is increased by increasing the bit depth.

More bits gives more accuracy. Higher sampling rates gives more bandwidth.

So why don't we use 256 bits and 384Khz? Because we only need to cater to what humans can actually hear. 24 bits gives us arround 144 dB of dynamic range and 44.1Khz gives us arround 20Khz bandwdith. That is enough to cover what human ears can perceive.

UnderTow

ORIGINAL: bitflipper

Also check this out (more or less on topic): Ultra Tweeter

This is a tweeter that "produces no audible frequencies". Too bad I already blew my monitor budget on those useless ADAMs...

Lol! I wonder if there is actually anything inside those wooden boxes. That would really be quite a joke if they were just empty (or had some bogus piece of crap inside).

UnderTow

ORIGINAL: UnderTow

Oh here is a nicer sine wave animation: http://www.rkm.com.au/ANIMATIONS/animation-sine-wave.html

UnderTow

I could stare at that for hours. Well, several minutes, at least.


Oh, and your explanation that "You only need two points to perfectly define a circle. Adding any more points to the circle won't tell you anything extra about the circle." is brilliant. No math required. Did you come up with that one yourself, or steal it from a book?

Well I intend to use it in the future, and when I do I will give you credit.

I still wonder how he got his degree(s) then- in Germany they don't take abuse of titles lightly, and they don't really have Cardboard Colleges AFAIK.

What is his degree in? Not electrical engineering, I can assure you. Probably not in any of the physical sciences. Psychology, perhaps.

ORIGINAL: tarsier

Sorry I don't have some spectrum shots to show you, but yes there is stuff above 20kHz. I normally record at 44.1 or 48 kHz depending on final delivery format, but I was curious about the whole 96 kHz thing as well. So I did some recordings of cymbals with an Earthworks mic (flat response out to 30 kHz) into a MOTU 828 mkII at 96 kHz sample rate. There was plenty of stuff above 20 kHz that got recorded. Then I tried recording a clarinet, and there were still plenty of harmonics being recorded above 20 kHz. They were down around -85 dBFS and lower, but they were there.

So at least with that combination of mics/converters there was plenty of material being recorded above 20 kHz.

Here is a spectrum example of "Triangle" (instrument), recorded using 24/96:

http://img265.imageshack.us/img265/4561/triangle2496ci4.png


Junski

ORIGINAL: bitflipper
I can, however, recommend one source that did a pretty good job of explaining the Nyquist magic theorem -- a book by Nika Aldrich called "Digital Audio Explained for the Audio Engineer". Parts of it are mathematically intimidating, but he does a good job of illustrating how the audio is reconstructed from as few as two samples per cycle -- something that is not intuitive at all!

Until you have a chance to read the book, here's the bottom line, which you'll have to take on faith for now: Nyquist says that you can encode and subsequently recreate ANY waveform EXACTLY as long as you sample it slightly over twice the highest frequency you need to record.

Careful... That is what the Nyquist theory says. But it only holds true for infinite resolution sampling. In other words, the bit depth would have to be infinite to get the original waveform exactly. With digital audio, the devil is in the details so I'm afraid I have to be a stickler on this point. But 24 bits is more than enough.

Aldrich's book is excellent. Everyone should read it if they are doing digital audio. It has a few minor errors that I would quibble with, and I wish it went into greater depth on the D/A side of things because that's where the magic really happens (to me, anyway. The sync function is the whole reason it works, and I don't think the book even mentions it) but overall it's a truly terrific book.

bitflipper: I think tarsier has issue with the word "EXACTLY". He is right that it isn't 100% exact unless you have infinite resolution aka infinite bit depth but then rightly goes on to say that 24 bits is more than enough [for all practical purouses]. (Bit in brackets added by me). It is all about covering the human dynamic and frequency range. We don't need "EXACT" copies of the original because we humans can't tell the difference anyway.

I think it is usefull to repeat that sampling rate does not equal resolution. It equals bandwidth (assuming you don't want aliasing). Bit depth is what amounts to resolution.

I'd also like to repeat what has been said by many people: Only in audio do we go to such ridiculous over implementation of sampling theory. In fields where accurate results are MUCH more important like RADAR, Sonar (no pun intended), medical equipment, telecommunications, satelite positioning etc etc, engineers stick to the Nyquist theorem. It is only because audio is so subjective (aka we can NOT trust our hearing and our sound perception) that things have gotten so ridiculously out of hand. There is a certain amount of machismo and self-delusion in this field that unscrupulous manufacturers take full advanatage of.

UnderTow

Especially surprising because any principle supported by something as black-and-white as a mathematical proof should not engender debate at all.

Well spoken. Maybe that's why it's good that this thread recapitulates everything regarding the subject, and I get a chance to familiarize myself with the bogus arguments - once bitten, twice shy etc.

Therefore I don't think it's a waste of time or effort, not in the least.

BTW according to Einstein, if you travel long enough in one direction, you should end up where you started again, so essentially you only need one vector to describe a circle.

This was ofcourse topped by Richard Feynmann who pointed out you could theoritically explain the whole universe as one ubiquitous particle moving both forward and backward in time, meaning you could do all of reality with one pixel.

And all based on pretty solid math, Ricky could do his 'rithmatic awright.

[Thx for that link Tarsier, will devour it in small bites]

ORIGINAL: bitflipper
tarzier, I am not flaming you. I appreciate your thoughtful contributions to this and other threads. But I suspect (and I won't take it personally if you prove me wrong) you've bought in to the notion that there are exceptions to Nyquist when there are none.

No flame taken. By all means, call me out when I say something stupid. (not "if" but "when" ) But in this case you misunderstood me, sorry I wasn't more clear. UnderTow got my interpretation right, I was taking exception to the word "exactly". Whereas you were mostly talking about frequencies and sample rate, I wanted to emphasize the fact that we still can't get the original waveform "exactly" due to the quantization error which is a result of having "only" 24 bits to work with.

Thus, you can sample a 3 kHz sine wave at a 6 kHz sample rate and reconstruct it exactly except for the quantization error. And with 24 bits, the quantization error is not audible. Agree?

ORIGINAL: bitflipper

But in your example of a 3Khz wave sampled at 6KHz (assume a perfect reconstruction filter to keep it simple), you DO get an exact copy, because anything other than a 3KHz sine wave would have "illegal" harmonics in it. The key to the Nyquist theorem is that you CANNOT have frequencies higher than half the sample rate. There can be no quantization error because all of the harmonics have been removed.

If that 3KHz wave was square, for example, it could not be reconstructed from 6KHz samples. It would no longer be a square wave because the harmonics would have been removed. You would indeed need a higher sample rate if that was your intent. But if we were only interested in frequencies up to 3KHz, and no higher, then we'd still be OK because for all practical purposes that's what we've got.

Don't think square waves or harmonics, think noise. Assuming a properly dithered system, the inaccuracies in the copy, also called distortion, is noise.

UnderTow

I don't know why I'm always drawn to this debate. Been in almost every one of 'em on this board... and quite a few on other boards. I've learned tons. Bought Apogee converters for great AD/DA filters and now almost any sample rate sounds the same in my studio. I will say that I hear a slight improvement at higher sample rates in my studio, but I don't hear that improvement on the final 44/16 CD. It's not worth the cost in resources on my DAW and I HATE waiting for bounces and exports at high sample rates.

And then there's this:

http://forum.cakewalk.com/fb.asp?m=53631

Try that test in your studio. This null test shows that it is possible for a 44.1khz file to contain the same AUDIBLE information as the 88.1khz file. The data that is not nulled against the imported 44.1khz file is still there, but either your system can't reproduce it, or you can't hear it, or both!

The quality/ability of the converters at different sample rates is a different issue.

ORIGINAL: bitflipper
But in your example of a 3Khz wave sampled at 6KHz (assume a perfect reconstruction filter to keep it simple), you DO get an exact copy, because anything other than a 3KHz sine wave would have "illegal" harmonics in it.

Not quite. If you had an infinite number of bits, then you do get an EXACT copy. But you don't have an infinite number of bits. And since the sine wave that is exactly half the sample rate is even trickier to conceptualize, let's go simpler. a 1 kHz sine sampled at 6 kHz--although the numbers aren't really important right now.

Let's assume that it is a perfect 1 kHz sine wave, no extra frequencies/harmonics/noise. You then sample it at 6 kHz. Most likely the amplitude of the sine wave at the given moment in time represented by the sampling clock (not the peak amplitude, but the continuous amplitude) will not correspond exactly to one of the quantization steps of the digital representation. (not one of the sampling steps, one of the quantization steps--bits, not sample rate) The amplitude has to be rounded up or down to the nearest sample value. That is the quantization error and it then becomes a part of the sampled signal. It is a form of noise, a form of distortion, a form of harmonics--non-harmonic harmonics. But I'll call it quantization error.

The key to the Nyquist theorem is that you CANNOT have frequencies higher than half the sample rate.

Agreed.

There can be no quantization error because all of the harmonics have been removed.

Disagreed. Quantization error has nothing to do with harmonics of the signal. It has everything to do with the signal itself. Even in the case of the perfect 1 kHz sine sampled at 6 kHz (which has no other harmonics, yes?) there will be quantization error because of the rounding of the amplitude up or down to the nearest sample value. Unless you have infinite bits in which case there's no need to round either way.

Now forgive me for snipping out the rest of your post that I agree with.

...
The real question in all of this is: is it necessary to record frequencies above 20KHz?

I had the pleasure of learning digital audio from Dr. Tom Stockham, and he did all his final work at 16 bit 50 kHz. He thought the 44.1 kHz CD rate was a big mistake due to the difficulty of filter design, but 50 kHz should be sufficient for digital audio. I tend to agree, but since I can't do 50 do I round up to 88.1 or down to 48...? (actually with oversampling converters, the filter problem has been solved pretty well. So I record at 44.1 or 48)

I hope you don't think I'm beating this to death. I'm just trying to clear up misunderstandings. Whether I'm misunderstanding you, or vice versa.

I don't understand. Why would your mastering project not be at the same sample rate as the imported stereo files?