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what do bits and Mhz mean? (1 Viewer)

Saurav

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Back in college, I know I studied and made it a point to understand Nyquist's theorem and the proof behind it. However, I don't remember any of that now.
but if my assumption above is right (that sampling frequency has little to do with the frequency of the sound being reproduced)
If you believe Nyquist's theorem (which AFAIK most of the scientific community does), then your assumption is wrong - the sampling frequency has everything to do with the highest frequency that can be produced. Or more accurately, the highest frequency that can be recorded. It's possible that a system chooses to record up to a certain frequency, but play back only up to 20 KHz, but that doesn't make sense - why record information that isn't being used?
So, there's two ways to look at this - first, question Nyquist's theorem in the first place. If he is wrong, then 48/96 KHz makes perfect sense - take more samples to get a more accurate reproduction. This is intuitively right - more frequent samples must obviously lead to a smoother output, right? However, Nyquist did prove, mathematically, that you don't need to sample any higher than 2x the highest frequency. Maybe his proof was in error... I cannot make a judgement on that.
The other way to look at this is that human hearing does respond to frequencies above 20 KHz. That would explain the benefits of a higher sampling frequency too, except for one catch - most modern speakers (and amps too, sometimes) do not go much beyond 20 KHz, so that raises the same question as above, what's the point of recording information that you cannot play back.
I also remember something from college called "Causal Filters" - the idea was that most of the math done with filters is valid for time values ranging from negative to positive infinity. However, no filter produces output from the beginning till the end of time - a filter can only produce output when an input is applied to it. I don't remember quite how this was handled in the math, but I wonder if something like this could affect Nyquist's theorem. That is to say, the theorem is valid if you're sampling a signal which extends backwards and forwards in time infinitely, but since no real signal does that, maybe that affects the theorem in some way. This is just a guess.
 

AlbertA

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Saurav:
That was my point. That someone figured
by experiments that 3.5Khz was enough to capture the
human voice. I know it doesn't conflict with Nyquist
theorem( as longs as you bandlimit the voice signal to
3.5 Khz, otherwise as you know we would have terrible
alias noise). And yes, telephone companies want to
pack as many voice calls as they can, we have designed
a lot of systems in class based on these assumptions.
Wheter or not we can hear above 20Khz or have any effects
due to it, it's still highly debatable. Some believe that
if a 22 Khz tone is introduced into a piece of music, one
will perceive it to sound more crisp.
Kieran:
I think DVD uses straight PCM. Then Lossless compression is
applied to the PCM codewords. This is something that could have been applied to CD-audio also. Why didn't they? I again, don't know. They could have applied simple huffman coding at least.
We do hear the harmonics contained in the voice, that's what
it makes all instruments distinguishable from the other.
I am currently working on a hardware synthesizer using physical modeling to emulate the physics of an instrument.
So I understand how the lack or incorrect placement of harmonics might change the perceived instrument.
BurkeP:
Yes, 44.1 Khz is the sampling rate for CD PCM audio.
You can ideally reproduce a continuous signal from it's samples, if the samples were taken at least twice of what the highest frequency component of the continous signal contained(that is the sampling frequency).And this is know as the Nyquist sampling theorem.(Emphasizing again-- this is only for the ideal case).
The sampling rate is not filtered. I was refering to the reconstruction filter. This is needed, since sampling creates a periodic repetition of the original signal.
Therefore the need for a guardband.
 

AlbertA

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Saurav:
Yes, brick wall filters require "knowledge of the
future" so to speak. That is their impulse response
extends across all time( a "sinc" response).
The only physically realizable filters are causal filters.
That is filters that do not need to know the future to compute the value of the present. I hope that makes sense.
It affects the theorem in that to reconstruct the signal
of bandwidth W, sampled at 2W, you need an ideal(brickwall) filter.
Here is a link that explains sampling:Link Removed
 

Kieran Coghlan

Second Unit
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Albert:
I think DVD uses straight PCM. Then Lossless compression is applied to the PCM codewords. This is something that could have been applied to CD-audio also. Why didn't they? I again, don't know.
They probably didn't apply lossless compression to the CD format, because it hadn't been invented yet. MLP was invented specifically for dvd-audio. I know that lossless compression has been around for a long time, but I doubt there were very effective versions of it in the mid 70's when the CD-A standard was being developed. Sure they could apply MLP or similar to CD *now* but why bother? DVD is surging forward, why try to squeeze more out of the CD medium when its end is in sight?
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Saurav

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It affects the theorem in that to reconstruct the signal of bandwidth W, sampled at 2W, you need an ideal(brickwall) filter.
Is this because of the "periodic repetitions" introduced by the sampling? If so, and since brick-wall filters aren't realizable in real life, could this be the reason for higher sampling rates? It would make the guard band wider, since the signal would repeat at a higher frequency, and this would allow a real-world filter to better remove the repeated component(s)?
This isn't the first time I've wished I paid more attention in my electronics classes :)
 

Ryan Schnacke

Supporting Actor
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Feb 5, 2001
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[Edit] Feel free to skip the post since much of what I said was posted while I was authoring [/Edit]
Saurav,
Yeah, you're right about causality and filters. This stuff is starting to come back to me. The inverse Fourier transform of a "brick wall filter" would have a response that begins before the event that caused it. So it would, in effect, be predicting the signal before it happened. That can't occur, so that's why we don't have "brick wall filters".
I don't think this next part has been discussed yet:
If we sample at 40kHz and there happens to be a signal of greater than 20kHz then we won't sample it correctly. As previously mentioned, we need 2 samples per cycle to correctly reconstruct this waveform later. But with a frequency > 1/2 Sampling frequency we won't get 2 samples per cycle. So we'll get a "picket fence" effect when we sample it. And when we reconstruct it the signal gets reflected around the Nyquist frequency to look like a slower frequency. And that's distortion.
Here's and example:
We're sampling at 40kHz and our music content is 20kHz and below. But there's some extra signal at 24kHz. The Nyquist freq is 20kHz (1/2 sampling freq). So the 24kHz signal will be reconstructed as a 16kHz signal.
So how do we prevent this picket-fence effect from causing distortions in our recordings? We filter. If we want to record up to 20kHz signals, then we filter everything above 20kHz. Use a filter with a nice steep slope so that by 22kHz there's practically nothing passing. Then sample at 44kHz so that the signals up to 22kHz won't get reflected.
Sooooo to make a long story short, the sampling frequency 44.1kHz was used because of our imperfect filters.
[Edited last by Ryan Schnacke on July 19, 2001 at 05:20 PM]
 

Kieran Coghlan

Second Unit
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Albert: Ha! I love it! a "basic" tutorial of sampling theory... and it only requires about 3 years of college level math to even read the formulae! Fortunately, I just took a graduate course in advanced math for Mechanical Engineers, so I could read most of that. But methinks that link is way beyond what most people here even want to look at, let alone try to read!
wink.gif

My favorite moment in studying advanced math was when "convolution theory" was introduced. "THATS IT!!" I said to myself... math is convoluted enough as it is, but if this stuff is bad enough that the mathemeticians see fit to NAME it "convolution"... I ... AM ... OUTTAHERE! :D Or in the famous words of Popeye, "Eye's had all's eye can stands, and eye can't stands NO MORE!!!"
Of course, there were still several weeks left to the semester, so I stuck it out, and convolution wasn't so convoluted after all, but I sure thought it was funny at the time... :)
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-Kieran
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AlbertA

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Saurav:
Yes, that's exactly the reason why one samples
higher than ideally needed. The higher the sampling
frequency, the less sharp the slope of the filter has to
be. Although, for music, the vastly increased sampling frequency and the new receivers with 100 Khz bandwidth seem to indicate that freqs. above 20 Khz are going to be reproduced in the near future, with new speakers of course.
I'm sure dogs will appreciate it(I can hear 'em now barking for no reason).
Kieran: Lossless compression already existed.
Simple compression would at least would have increased
the CD storage by 1.5 times. Not much, but engineers always try to squeeze every little performance we can. This should of course be done on the beginning, I agree, not now when the format is very mature.
 

Saurav

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This brings back memories *grin* I know when I threw up my hands and gave up - Contour Integrals. Integrating values over a 3D surface that looks like a doughnut (a toroid, to be more specific).
I hope we engineers aren't sounding like we're showing off all our advanced math skills (or lack thereof, actually), to the non-engineers here :) Seriously, if we are, I apologize.
That is, if anyone who's not an electronics/computer engineer is still reading this thread..... :)
 

AlbertA

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Contour Integrals. Yes I remember from my
electromagnetics class.
Well, I hope everyone is reading, If it helps
to understand the decisions engineers make.
I chose that sampling tutorial because it's
very brief and complete. And it comes from
one of the gurus of audio synthesis and audio DSP: Dr.
Julius Smith.
Well, I think we have deviated enough from
the original question.
If anyone is interested in more depth info
email me at: [email protected]
 

Kieran Coghlan

Second Unit
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Oct 26, 1998
Messages
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Ryan, great post! (I only just realized that it was there... you snuck in at the top of the second page... I didn't even realize we'd gone to a second page!) What you said may have been already stated, but only if one was good enough to go back and pick out all the pieces... Thanks. What you said about why we use filters, and why 44.1kHz was chosen, came to me as I was writing one of my previous posts, but I don't think I expressed it as succinctly as you.
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-Kieran
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RicP

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This has been a superb thread, full of informative answers by very bright people. :)
If the HTF admins don't archive this thread I will on my site. :)
Keep the good information flowing. :)
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Ric Perrott
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My Theater ;My DVD's
 

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