Sampling/Time Resolution - In search of sources Options

[FreaqyFrequency]

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!

[Woodinville]

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.

[Northpack]

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.

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

This post has been edited by Northpack: Oct 9 2011, 11:46

[Woodinville]

That's very interesting. I never realized that it actually can't be infinite as some textbooks say oversimplifying.

Well, consider, there is always noise, and the signal slope is not infinite, there has to be some error. Not much, maybe, but some.

Having infinite slope means having infinite frequency, and that last quantum that takes up the mass-energy of the entire universe kinda gets to be a problem, and that's still not infinite.

So, in the real world, nothing is perfect, including "nothing".