[Edmund[_2_]]

On Fri, 15 Feb 2013 15:04:03 +0000, Dick Pierce wrote:

Edmund wrote:
On Thu, 14 Feb 2013 22:14:07 +0000, Dick Pierce wrote:


Scott wrote:

On Wednesday, February 13, 2013 7:41:41 PM UTC-8, Dick Pierce wrote:

Scott wrote:

"The Nyquist theorem (which is mathematically proven) says that the
exact waveform can be reproduced if the original signal is frequency
limited to less than half the sampling frequency."

The quote you supplied does NOT say that "digital is perfect."

In effect it does.

To you. It does not to me. It simply, to me, states that when the
nyquist criteria is met, and that means the signal must be limited to
less than half the sampling rate, samplig does NOT lose any information
needed to reproduce an exact replica of the signal meeting the
criterion.


So if I offer you an analog signal, limited to 40kHz you can sample
that at 80 kHz and 4 bit, you can recreate the input signal exactly?
Well, would you like to prove that?

You just went and changed the conditions. To this point, all the
discussion had to do with sampling. One other poster is clearly confused
about the difference between sampling in the time domain and
quantization in the amplitude domain, and it appears that you have
similarly bundled the two together as well.

Let's examine your statement, for it contains several errors:

"So if I offer you an analog signal, limited to 40kHz you can sample
that at 80 kHz

First error, the bandwidth must be limited to LESS THAN HALF the sample
rate, NOT half the sample rate.

I am not sure but If my memory serves me well one need at least twice the
highest frequency as sample rate.
In your terms LESS OR EQUAL TO HALF THE SAMPLE RATE.
Correct me if you are sure that I am wrong.

"and 4 bit"

Second error, just like in the sampling error above, you made an
assumption about the signal which may, in fact, not be true. Now IF the
dynamic range is limited to 24 dB, then with proper dithering, yes, all
of the information present in the original signal WILL be available at
the output of the system.

Well you did not mention the dynamic range at all.

----------------

"The Nyquist theorem (which is mathematically proven) says
that the exact waveform can be reproduced if the original
signal is frequency limited to less than half the sampling frequency."

------------------------

And I don't think that is right.




Now, the separation between sampling and quantization is NOT some clever
symantic trick, rather it is at the very basis of the process. If it
helps, you can think of the sampling process as quantization in the time
domain, and what many here term "quantization" as quantization in the
amplitude domain. Assuming the wo are inextricably tied together is the
root of much confusion, as exhibited by your question as one example.

Let's rephrase your question slightly,

No lets not do that.
Stick to what I asked which is an analog signal.

Edmund