[Digitalchkn]

 
Well, either a) the signal must be finite in length, (i.e., at some point for t < t_0, x(t)==0 and for t > t_end, x(t) ==0). Here's a link to a university lecture that discusses energy in signals (http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/5_10node10.html). Here they require a finite length signal.
 
 
Or b) you can talk about the signal's energy per unit time. I believe this is the more typical case. Here, Parseval's theorem is useful for showing that the energy in the signal is the same whether you calculate it in time domain or Fourier domain (http://en.wikipedia.org/wiki/Parseval%27s_theorem). One might do this by considering the energy of some periodic signal. One integrates over the period of the signal.
 
The energy in the signal is bounded if the energy in the Fourier coefficients decrease sufficiently fast with increasing wavenumber. In the case of a band-limited signal, this is the case, because all Fourier coefficients are zero beyond the Nyquist frequency.
 
Cheers

 
 
 

   
It's also been a while for me, but something like a sinusoid over infinite time does have infinite energy. (Think of a voltage signal like that operating for eternity—you'd need an infinite amount of energy from some source to keep applying that voltage across a resistor or something.) That's why these are analyzed in terms of power, so divide by the time of integration. If you're not integrating over infinite time and you're not integrating something that's going to infinity in nasty ways, then the integral will be finite.
 
Look at power spectral density, etc. and see if there is nonzero content at frequencies above Nyquist. Or just filter those frequencies out, depending on the application.
 
 

 
Amazing how the fundamentals slip out your head after some time.  You guys more or less covered it for me. Something along the lines of a certain class of energy signals that fall into category of power signals which can still be analyzed using fourier integration without blowing up, if I recall correctly.  Gets you that delta functions as a consequence, as a sort of a limit.
 
Anyways, this was a bit off topic. The phrase "all real signals are finite energy" triggered the question for me.

 

[Digitalchkn]

 
Yes, I suppose we can get into if you like. You asked what I meant by "quality equipment".  The equipment is clearly specified in the video.  If you have the idea we are acting as if we can discern 16 bit precision on a scope, well, neither I nor the video made any such claim.  By quality I meant an analog based source for highly precise, very low distortion test signals and analog based, highly precise, very low distortion spectrum analyzers.  Things that were obvious on a scope are things like the idea you don't get good clean sine waves out of AD/DA conversion using only slightly more than 2 samples per wave.  You do.  You couldn't specify it was .05% distortion looking at the scope.  Combine it with a spectrum analyzer and you can see there no large levels of distortion either.  Straightforward stuff indeed.
 
The premise of the video is if you don't know or don't believe digital can do what it claims as cleanly as it claims you can investigate with good analog equipment what it can and what it cannot do.  The analog results show that up to 20khz digital is as clean and accurate as it claims to be.  Of course any such introductory type video isn't in depth or detail for any tiny issue one may have with digital audio.  But one could do the same thing if they wished and investigate whichever issue they think they are having.
 
So with your advanced knowledge and literacy in things digital what are the problems of digital processing in audio?

 
In the context of this thread, this video may be interpreted too literally and one may conclude that based on the experiments that bit depths and sample rates shown are more than sufficient. Consequently, those continue to argue that conclusions in this video is gospel.
 
Or put it another way, if I wanted to very the quality of my ADC/DAC path in my designs I would be give it a lot of thought about measurement equipment used, considering that noise floor and/or resolution of many instruments is at or worse than the levels of what I am trying to measure.

 

[bigshot]

  In the context of this thread, this video may be interpreted too literally and one may conclude that based on the experiments that bit depths and sample rates shown are more than sufficient.

 
Uh... yeah. Is there something there I'm not hearing? Is what I don't hear what we're talking about? Should I care about what I can't hear?

 

[bigshot]

   
Is that Kirk Hammett? Of Metallica?

 
Dashiell. Add that to your reading list before you can use the English language!

 

[esldude]

   
In the context of this thread, this video may be interpreted too literally and one may conclude that based on the experiments that bit depths and sample rates shown are more than sufficient. Consequently, those continue to argue that conclusions in this video is gospel.
 
Or put it another way, if I wanted to very the quality of my ADC/DAC path in my designs I would be give it a lot of thought about measurement equipment used, considering that noise floor and/or resolution of many instruments is at or worse than the levels of what I am trying to measure.

Okay, so are you saying 44.1 khz sample rates or 16 or 24 bit depth is not sufficient?  What part of digital audio's performance envelope fails to be good enough for human audio?
 
The video is not gospel.  I do not find much to argue with considering what it shows and claims. 
 
I understand that to verify the complete depths of your AD/DA path you need instruments cleaner than what is tested.  In the case of the video that appears to not be the case.  But it does show the basic AD/DA path is clean enough it appeared not to corrupt the quite clean analog signals in use.  Making you think the AD/DA path was at least equal or better than the analog sources.  It shows the AD/DA path is transparent to quite low levels of degradation.  Since they were using a cheap, obsolete consumer level AD/DA unit, it seems sufficient to show digital largely works as claimed.  Better implementations would most likely reach closer to the theoretical limits of a digitally sampled system.   You seem to be working pretty hard not to agree.  What is your opinion of where it falls flat? Or is that your opinion?  Or do you just dislike video presentations?

 

[RazorJack]

That video made so much sense to me, I'd say it almost put my DSP and other EE-related courses I had to follow in college to shame, when it comes to explaining a relatively complex matter (for the average Joe, not engineers) in straight forward language.
 

  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
 
<snip>
 
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.

 

 

[Digitalchkn]

 
Okay, so are you saying 44.1 khz sample rates or 16 or 24 bit depth is not sufficient?  What part of digital audio's performance envelope fails to be good enough for human audio?
 
The video is not gospel.  I do not find much to argue with considering what it shows and claims.
 
I understand that to verify the complete depths of your AD/DA path you need instruments cleaner than what is tested.  In the case of the video that appears to not be the case.  But it does show the basic AD/DA path is clean enough it appeared not to corrupt the quite clean analog signals in use.  Making you think the AD/DA path was at least equal or better than the analog sources.  It shows the AD/DA path is transparent to quite low levels of degradation.  Since they were using a cheap, obsolete consumer level AD/DA unit, it seems sufficient to show digital largely works as claimed.  Better implementations would most likely reach closer to the theoretical limits of a digitally sampled system.   You seem to be working pretty hard not to agree.  What is your opinion of where it falls flat? Or is that your opinion?  Or do you just dislike video presentations?

 
Summarizing point? no longer a reason for 16/44 as the ultimate distribution format for consumers.
 
To answer your first two questions we would need assign a metric to the digital audio performance captured vs a given format. Personally, I am not aware of a generally accepted metric that we all can agree on.
 
Side-point: by now everyone has seen this video. Things works largely as claimed (surprise). The devil is in the details, which seems to me to be the crux of the matter

 

[bigshot]

  To answer your first two questions we would need assign a metric to the digital audio performance captured vs a given format. Personally, I am not aware of a generally accepted metric that we all can agree on.

 
I agree on the metric of audibility. How about you? Does that work?
 
Ignoring everything but what human beings can hear, for the purposes of playing back music in the home is there any reason to use rates above 16/44? That seems like a really simple question to answer to me.

 

[Digitalchkn]

   
I agree on the metric of audibility. How about you? Does that work?
 
Ignoring everything but what human beings can hear, for the purposes of playing back music in the home is there any reason to use rates above 16/44? That seems like a really simple question to answer to me.

 
Let's break this down first. We need to understand our bandwidth and dynamic range requirements. What is it that humans can and cannot detect? As in not resolve into music, but simply perceive as a mechanical vibrations of air. Do we have a consensus on what these requirements are?

 

[esldude]

   
Let's break this down first. We need to understand our bandwidth and dynamic range requirements. What is it that humans can and cannot detect? As in not resolve into music, but simply perceive as a mechanical vibrations of air. Do we have a consensus on what these requirements are?

Well I believe there have been a couple people who could perceive 25 khz at very high levels (more than 100 db) in otherwise quiet surroundings.  A very small percentage of young adults have been shown to hear 22-24  khz at similar very high threshold levels.  That is why JJ Johnston or Robert Stuart say 60-65 khz sampling rates would have been the most possibly needed if one wishes to leave nothing on the table.  Nyquist for 25 khz with room for filtering easily.  That is needed however for probably less than .1% of the adult population. 
 
As for dynamic range, it is few and far between finding electronics with more than 120 db SNR.  So 24 bits should be fine, theoretically there may be situations where 16 could fall short.   It will get mentioned that 120 db is the threshold of pain.  I don't know if you could be expected to hear more loudly than that even though it hurts.  I believe the answer is yes.  I also believe it makes no sense to decide to produce audio playback with that extra pain inducing dynamic range. 
 
So you could say we need response to 25 khz and 20 bits to be sure of full transparency without question.  For such people 88/24 should be more than enough.   Does it make sense to have standard delivery mediums that more than double file size to satisfy the less than 1% who could hear it likely far less than 1% of their time listening?

 

[groovyd]

 

I highly recommend "Discrete-Time Signal Processing" by A. Oppenheim and R. Schafer 3rd edition

 
+1 excellent graduate level text

 

[groovyd]

  The devil is in the details, which seems to me to be the crux of the matter

 
+1 - actually entertaining that such a group of people who pretend to know signal processing to the point of arguing over equations that have nothing to do with the reality of the topic don't even recognize where their misplaced theories fall apart in applied science.  it is good though to see at least one other true signal processing guy around

 

[bigshot]

   
Let's break this down first. We need to understand our bandwidth and dynamic range requirements. What is it that humans can and cannot detect? As in not resolve into music, but simply perceive as a mechanical vibrations of air. Do we have a consensus on what these requirements are?

 
Here's a start. If you have anything to add, I can update it.
 
http://www.head-fi.org/t/645851/the-most-important-spec-sheet-the-human-ear

 

[bigshot]

 
Well I believe there have been a couple people who could perceive 25 khz at very high levels

 
As sound pressure, not music.

 

[ab initio]

Amazing how the fundamentals slip out your head after some time.  You guys more or less covered it for me. Something along the lines of a certain class of energy signals that fall into category of power signals which can still be analyzed using fourier integration without blowing up, if I recall correctly.  Gets you that delta functions as a consequence, as a sort of a limit.

Anyways, this was a bit off topic. The phrase "all real signals are finite energy" triggered the question for me.

What on earth are you rambling About?