[Digitalchkn]

 

 

 

One reason the video is instructive even to those who don't know, understand or care to be bothered by the theory is how it is all checked with quality equipment in the analog realm.

 
Can we elaborate on the term "quality equipment"? I hope there is an understanding that the dynamic range of waveforms shown on analog scopes is nowhere near that of even 16 bits.
 
There is no doubt in my mind the video is a great introduction into the subject. There are other details at play that requires more in-depth look. Hence, professors in IEEE.

 

[groovyd]

  Watch this video.  I am beginning to think it should be required viewing before one can post about digital audio.
 
http://www.xiph.org/video/vid2.shtml
 
Not singling you out personally, but your post contains several fallacies which are repeated millions of times.  Watch and understand this 23 minute video, and you will get why they are false.  Not false just in theory, but in actuality.  Two or more samples is enough to fully reconstruct the signal, and one and only one waveform fits any possible combination of samples as long as no frequencies exceed half the sample rate.  Yes, filters are imperfect, and reconstruction falls just a bit short of perfect theory.  But most the of the important factors have been dealt with.  We can get something like 95% or more of what is predicted by theory and put the last few percent of inaccuracies in a place where humans do not hear them.  Effectively, audibly very, very close to 100% fidelity to humans in actual use. 
 
You can go to 96 khz if you just really, really, really want to be sure.  There certainly seems close to zero point, and beyond 96khz there is zero point.  It has never been shown in a credible repeatable test that people hear 96 khz vs 48 or even 44 khz.  Null results so far.

 
Having passed my masters in digital signal processing with flying colors I respectfully disagree with you and that link.  I can easily fit an infinite number of near sine waves into a set of samples at twice its frequency without even introducing the concept of sample phase.  Introducing sample phase gives me yet another infinite set of this time absolutely perfect sine waves to choose from.  Of course this assumes nobody cares about phase either in addition to amplitude.  In fact, as sample phase approaches integer multiples of pi the variety of near-perfect sine waves that fit the samples approaches infinity.  What this means is your filter must be dead nuts perfect to even have a chance of reconstructing one of an infinite number of phase shifted sine waves that 'might' be correct but absolutely is not with inverse probability to sample phase.  
 
Sure, mathematically only one wave fits if: 1) sample phase is not a multiple of pi and 2) it is an absolute perfect sine wave and 3) you are assuming perfect brick wall filters with zero phase shift.
 Unfortunately none of these conditions even remotely represent a real system in any way.  Yours is a straw man argument that I won't argue with anymore... you can make believe whatever you want.

 

[castleofargh]

  in theory 48khz allows for a 24khz bandwidth of which they say humans only have about 20khz range of hearing.  so the extra 4k would be for good measure but the reality is all of this makes a number of assumptions that are not true in a real system.
 
recognizing nyquist theory is one thing but if you think for a second about how that sampled waveform will look you see that 2 samples per cycle is really not enough even at a minimum.  take a 1hz sine wave and sample it 2 times per cycle.  it is entirely possible that both of your samples fall at EXACTLY the two zero crossings that occur in every cycle once on the way up and again on the way down and your reconstructed output becomes a flat line. by this it becomes pretty clear to see that 2 samples per cycle really is not enough at all to reconstruct your sine wave.  nyquist theory assumes a number of ideal conditions, none of which hold in a real sampling system.  it merely represents an absolute bottom line minimum spec requirement if you want to represent ANY of the information at a certain frequency but not necessarily all of it in all circumstances.  infact given 2 samples per wave taken at any point in the cycle i can draw for you an infinite number of possible near sine waves of different amplitudes that pass through those points.  lets assume the amplitude of the signal matters.  by raising the sample rate beyond the nyquist rate you quickly begin to remove the singularities and the multitude of waveforms that fit the samples for a given frequency and you allow breathing room for the realities of the limitations of a real sampling system, such as non-ideal pre-ADC bandpass and post-DAC reconstruction filtering.
 
if we assume 20khz is a reasonable limitation of human hearing without regard for the fact that our amp, speakers, etc further attenuate the response at these edge of spec frequencies
then 48khz is really still an absolute minimum. in my opinion 96khz gives plenty of breathing room to counter all of the additive realities of a true system from end to end. 

I tend to disagree, but let's say you're right, bad luck we get only one or even no usable sample, then your example would make some crap for 1 and only 1 period of a 22.05khz sine. a sine that will be cut out by the low pass filter anyway.
and for everything lower, your example becomes false as every other frequencies will get more than 2 points of reference with 44.1khz. that 1khz sine will get 44 samples, it's gonna be hard to misinterpret that one when 2 could be enough.
I am still in favor for 48khz to be sure that no one will mess up the low pass filter. but it's more as a security against pieces of gear done badly than a real need. doubling everything for "just in case" peace of mind at frequencies most of us don't hear, on audio systems that roll them off or cut them out, I fail to see the point.
 

 

   
There is not plenty of energy beyond 20kHz with acoustic instruments.

 
I have spectrum analyzed lots of commercial "hi-rez" classical and jazz and saw that modern systems can pick up spectral content to no less than 30KHz. Even older recordings made during the infancy of magnetic medium have a positive SNR beyond 20KHz.
 
Basically if you take your redbook audio  recording of your acoustic instrument and your 22.05KHz frequency point is wiggling in your spectrum analyzer then there bound to be energy beyond 22.05KHz. It's a different debate whether you or I are able to hear a test tone up there or not.
 
As an engineer, I ask myself how much deterministic energy is up there and if it's sufficiently large then I would want to capture it.  Oddly enough, I have yet to see some  analysis tool that plots integrated energy(power) over frequency as it applies to audio applications. That would allow one to determine 90 or 95% bandwidth requirements.

I understand the idea, but I'm completely against it for the exact reason you want it. I see that as an added chance to damage my hearing, and even though the sound pressure and duration are what count most, high freqs have more energy for the same amplitude right? I remember reading something about violin players and hearing loss where instruments making high frequencies were seen as more dangerous overall. and some hearing protection dealer saying that what was most important was to stop high freqs when they made some for me.
I really do not want my ears to receive too much of something I don't hear, but could still had damages on the long run.
 
well in my case it's not a real problem as pretty much none of my headphones/IEMs are able to deal with 20khz anyway, and most IEMs I've owned were almost dead silent above 14 or 15khz ^_^.

 

[bigshot]

 
Sure. That's why, as a consumer, you make a choice. Your choice may differ from choice of others who may find benefit from a, say, 24/48 setup.

 
My dog can't afford a stereo.

 

[Digitalchkn]

   
My dog can't afford a stereo.

 
Didn't know your dog has the final say on your purchasing decisions

 

[bigshot]

  I am still in favor for 48khz to be sure that no one will mess up the low pass filter. but it's more as a security against pieces of gear done badly than a real need. doubling everything for "just in case" peace of mind at frequencies most of us don't hear, on audio systems that roll them off or cut them out, I fail to see the point.

 
Isn't it nice that we all make different compromises... and all those compromises are beyond the range of our ability to hear! It makes it easy. Any decision on where to compromise is the right decision. (Dogs and bats notwithstanding, of course.)

 

[groovyd]

  ... I fail to see the point.
 
pretty much none of my headphones/IEMs are able to deal with 20khz anyway, and most IEMs I've owned were almost dead silent above 14 or 15khz ^_^.

 
agreed.
 
and also in failing to see the point of manufacturers saving a few cents to not produce equipment that outperforms the music it will be used with.  ofcourse this is head-fi and some people do manage to find crystalized gold connectors that are dubious at best to improve the sound in any meaningful way when adding a few more bits to the source file would have a much more dramatic impact for let's just round down and call it free.  in this day and age there is no good argument to not increase both the sample rate and bit depth of recorded music as a common standard. 

 

[bigshot]

   
Didn't know your dog has the final say on your purchasing decisions

 
I buy my own stereo and he mooches music off of me. Haven't heard him complain about the lack of sound that is completely inaudible to human ears yet.

 

[Digitalchkn]

  I understand the idea, but I'm completely against it for the exact reason you want it. I see that as an added chance to damage my hearing, and even though the sound pressure and duration are what count most, high freqs have more energy for the same amplitude right? I remember reading something about violin players and hearing loss where instruments making high frequencies were seen as more dangerous overall. and some hearing protection dealer saying that what was most important was to stop high freqs when they made some for me.
I really do not want my ears to receive too much of something I don't hear, but could still had damages on the long run.
 

 
Luckily high frequency content tends to falls off. And I am not talking about your sound system reproducing gamma rays. But yeah, point taken.

 

[bigshot]

  in this day and age there is no good argument to not increase both the sample rate and bit depth of recorded music as a common standard. 

 
Isn't "you can't hear the difference anyway" a good enough argument?
 

  Luckily high frequency content tends to falls off.
 

 
Wait a minute! A few posts back didn't you argue that there was plenty of content up there?

 

[Digitalchkn]

   
 in this day and age there is no good argument to not increase both the sample rate and bit depth of recorded music as a common standard.

 
++

 

[Digitalchkn]

   
Haven't heard him complain about the lack of sound that is completely inaudible to human ears yet.

 
Well I guess he's not going to post on this forum anytime soon then.

 

[Digitalchkn]

   
Wait a minute! A few posts back didn't you argue that there was plenty of content up there?

 
There is plenty of content beyond 20KHz. It just falls off ... eventually.

 

[bigshot]

At some point it becomes radio waves and your stereo can receive it again, right?!

 

[bigshot]

   
Well I guess he's not going to post on this forum anytime soon then.

 
Here is my woofer.