|oh man. i tried so hard not to get sucked into this debate. but here i am.|
the connect the dot explanation does help to explain how it's done, but the reason that does not quite work is just that the Max and Min points of the source are very unlikely to be the 2 points sampled. You have the same chance of sampling at the zero crossings. most likely the 2 samples per cycle are going to hit during it's ascending and descending, and get no information about max or min.
Can a 44.1k sampling rate accurately PRODUCE a 20k wave?
Sure. The details of that wave are mostly lost, but it's frequency and amplitude are approximated pretty well.
Can a 44.1k sampling rate accurately RECORD a 20k wave?
Not as easily. The waveshape is sure to be lost and the amplitude is subject to mis-representation.
Do kids today care? Do they know what they are missing?
Probably not. I am 28 and had a record player growing up. I love the sound of 2 inch tape. I love the new DSD technology. I hate mp3s. I am (we are) the minority on audio quality preference. DSD has the potential to take over the recording industry in the next 5 years. If so PCM will be like our old friend the VHS. Unless handheld mini disc recorders take over first, then we are all doomed.
Did I get this question/answer format from watching seinfeld last night?
Yes. Yes I did.
On Dec 20, 2005, at 1:52 PM, Adrian Bartholomew wrote:
this is where SOME info is worse than NO info.
dude think about it.
u have a wave at 1/2 the sample frequency. think about it like connect-the-dots.
the only ones u can plot are the max(positive) and min(negative) points of the wave. NOW connect the dots and what do u have. thats right a sawtooth wave. even if the original was a sine.
but at least u have the frequency. forget about phase what about shape or tone?
even if u sampled at a frequency high enough to give u three or even 4 points to connect, its STILL approximate, very far from the shape of the original and certainly not "all the information of the original signal".
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On Dec 20, 2005, at 1:53 AM, Bill Fox wrote:
a k butler wrote:
Bell Labs researcher Harry Nyquist develops Sampling Theory. It states provides that if a signal is sampled at twice its nominal highest frequency, the samples will contain all of the information in the original signal.
Which is clearly not true :-)
There's no way to keep the phase information for a signal sampled
at only twice it's frequency.
Only the amplitude.
I guess that the Nyquist Theorum is misquoted somewhat here
Although you might be correct for a frequency of f when the sampling frequency is 2f, the theorem correctly stated says that it will be good for frquencies UP TO f Hz, i.e. not including f. So while you're correct for one frequency, f, the theorem holds 100% true for all frequencies below f and no information is lost. The mathematics bear out. For shorthand, the bandwidth of a system is stated as f Hz, not (f - 1) Hz.
BTW, I dare anyone to tell me they can HEAR that 20kHz has a wrong phase relationship in a system sampled at 40kHz. Plus, in the real world, where there are no ideal filters, a guard band is built in. That's why an audio system that is designed to have a 20kHz bandwidth uses a sampling frequency of 44.1kHz. This also avoids the problem of 20kHz not having a proper phase relationship since it is less than half the sampling frequency, not exaclty half the sampling frequency.