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Sampling/Time Resolution - In search of sources
FreaqyFrequency
post Oct 4 2011, 21:36
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Greetings all,

I've been lurking on these forums for about the last year, and I finally signed up today to pick the brains of some of the more knowledgeable individuals here.

On Saturday, I'm giving an 8 minute informative speech on the essential elements of digital audio (PCM to be exact, leaving DSD out given the time limit), why it was a logical progression from analog recording and storage technology, and a brief sketch of lossy/lossless implementations of it.

My primary objective at this point is to get a rock solid source, stating that (and why) any sampling rate is able to capture a given bandlimited source with perfect time resolution (ignoring frequency response and filtering in this case, dealing only with time). I was encouraged to touch upon this point in particular because of a presentation I found on YouTube a few months back, whose essential message was "Digital is bad because you hear the music as packets rather than as an analog waveform" and was advocating that everyone dispense with their digital media and go get a turntable and vinyls. My intent is to disprove the "packets" notion, and this source is the closest I have seen to doing that as of now:

http://www.tonmeister.ca/main/textbook/node639.html

If anyone could supply further documentation (or their own findings/conclusions on the matter), that would be most appreciated. Thanks! smile.gif
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Woodinville
post Oct 8 2011, 03:12
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The time resolution of a PROPERLY reconstructed PCM signal (note, if you take away the antiimaging filter the time resolution GETS WORSE!!) is approximately

1/ (2 pi fs nlevels)

for CD that is 1/( 2 pi 44100 65536).

Time reconstruction can not be perfect, because noise from quantization (by the way, also look up dithering, it's the level issue that also gets abused phenominally stupidly) creates a slight phase jitter.

This is, however, very small, i.e. on the order of 6 picoseconds give or take.

You'll also see the idea that "the sound is turned into stairsteps". This mistake comes from the fallacy that one can look at the signal before the antimaging filter and have it make sense. Somewhere out there I have a set of graphs to reply to that. Now let me see if I can find them.



This, of course, takes some explanation. The first (top) is the sine wave that results when you have ONLY the output from the DAC taht is below FS/2.

The next line adds either 2 or 4 images, I forget which (the squiggly line) and adds them to the sine wave, giving the rather odd lookign waveform.
Third line adds more.
The last line adds the first 1000 images. Notice that the result when it is added to the original signal, is the "stairstep" people whine about.

Every bit of that 'stairstep' except the original sine wave, however, results from frequencies above half the sampling rate, showing, once again, that Shannon was right.

You are welcome to grab the plot if you like.


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J. D. (jj) Johnston
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Northpack
post Oct 9 2011, 11:28
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QUOTE (Woodinville @ Oct 8 2011, 03:12) *
The time resolution of a PROPERLY reconstructed PCM signal (note, if you take away the antiimaging filter the time resolution GETS WORSE!!) is approximately

1/ (2 pi fs nlevels)

for CD that is 1/( 2 pi 44100 65536).

Time reconstruction can not be perfect, because noise from quantization (by the way, also look up dithering, it's the level issue that also gets abused phenominally stupidly) creates a slight phase jitter.

That's very interesting. I never realized that it actually can't be infinite as some textbooks say oversimplifying - but of course you would run into the paradox described by knutinh if it were. Another example that everything in nature and thus in our means to represent nature has to be quantized at some level.
QUOTE
I had missed the 2pi function in 1/(2pi*quant. levels*fs), so I guess that figure would actually be closer to 55 picoseconds. Either way, pretty far below the ability of any human being to distinguish a timing difference.

That's what you think. I bet there are some audiophiles living on a quantum time scale... oh, wait, then they couldn't claim that digital is bad because it's discrete wink.gif

This post has been edited by Northpack: Oct 9 2011, 11:46
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Posts in this topic
- FreaqyFrequency   Sampling/Time Resolution - In search of sources   Oct 4 2011, 21:36
- - saratoga   QUOTE (FreaqyFrequency @ Oct 4 2011, 16:3...   Oct 4 2011, 21:40
- - benski   http://www.dspguide.com/ch3/3.htm Another good to...   Oct 4 2011, 21:41
- - FreaqyFrequency   Wow, you guys are quick on the draw! Thorough...   Oct 4 2011, 21:56
- - C.R.Helmrich   Was about to post the link that benski already pos...   Oct 4 2011, 22:19
- - xnor   Some introductory wiki pages: Sampling Nyquist-Sha...   Oct 4 2011, 22:42
- - Speedskater   You might look through member "woodinville...   Oct 4 2011, 23:21
- - knutinh   It is called Shannon-Nyquist sampling theoreme, an...   Oct 5 2011, 01:44
- - Axon   All I can suggest is to read this section from the...   Oct 5 2011, 02:23
- - FreaqyFrequency   Again, many thanks for all the replies, extremely ...   Oct 5 2011, 03:14
|- - dhromed   QUOTE (FreaqyFrequency @ Oct 5 2011, 04:1...   Oct 5 2011, 09:25
|- - db1989   I, too, like that analogy—and dhromed’s! Thi...   Oct 5 2011, 19:54
- - drewfx   The critical piece of information to stress to ...   Oct 5 2011, 17:38
|- - benski   QUOTE (drewfx @ Oct 5 2011, 12:38) The cr...   Oct 5 2011, 18:02
|- - dhromed   QUOTE (drewfx @ Oct 5 2011, 18:38) When t...   Oct 6 2011, 10:03
- - FreaqyFrequency   That is a great analogy, and analogies will be a s...   Oct 5 2011, 19:02
- - DVDdoug   QUOTE When the digital signal is converted back to...   Oct 6 2011, 00:03
- - krabapple   If you want to see the sorts of trainwrecks that h...   Oct 6 2011, 01:22
|- - 2Bdecided   QUOTE (krabapple @ Oct 6 2011, 01:22) If ...   Oct 6 2011, 12:42
- - Woodinville   The time resolution of a PROPERLY reconstructed PC...   Oct 8 2011, 03:12
|- - Woodinville   QUOTE (Woodinville @ Oct 7 2011, 19:12) T...   Oct 9 2011, 00:04
|- - Northpack   QUOTE (Woodinville @ Oct 8 2011, 03:12) T...   Oct 9 2011, 11:28
|- - Woodinville   QUOTE (Northpack @ Oct 9 2011, 03:28) Tha...   Oct 9 2011, 11:45
- - FreaqyFrequency   Thank you very much JJ, I've been following yo...   Oct 8 2011, 17:33
- - FreaqyFrequency   So I was flipping through some of my documents as ...   Feb 12 2012, 23:47
- - MichaelW   As the thread has been resurrected, and as the mis...   Feb 13 2012, 01:48
- - 2Bdecided   QUOTE (MichaelW @ Feb 13 2012, 00:48) two...   Feb 13 2012, 16:12
- - knutinh   QUOTE (2Bdecided @ Feb 13 2012, 17:12) On...   Feb 13 2012, 22:21
- - MichaelW   QUOTE (2Bdecided @ Feb 14 2012, 04:12) Pr...   Feb 13 2012, 23:02


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