[Audio_Empire[_2_]]

On Friday, February 15, 2013 5:36:20 PM UTC-8, Dick Pierce wrote:
Audio_Empire wrote:
On Thursday, February 14, 2013 2:14:07 PM UTC-8, 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.


If I might chime in here. That's not exactly correct. It is correct
as far as it goes, but I'm sure that you didn't mean to infer that
a musical performance recorded in 8-bit 32 KHz sampling rate
is going adequately reconstruct the actual original waveform?
Even given that the highs would be truncated at about 15 KHz,
which was once considered part of the definition of High-
Fidelity, the dynamic range of such a quantization would be
limited to about 48 dB and distortion would be very high compared
to 16-bit, 44.1 KHz.

There seems to be a general,confusion he sampling and
quantization ARE |NOT the same thing: they are two separate
processes. You cna have one without the other, and you
can certainly treat and explore the two separately (despite
the fact that in most audio systems, the two work together).

As an aside, let me give some examples of one without the
other: first, a switched-capacitor filter is a discrete-
time sampled, continuous-amplitude system. No quantization
takes place. Another example in the audio realm is the
old classic bucket-brigade CCD analog delay lines, again,
a discrete-time sampled, continuous-amplitude system with
no quantization. And, for a very common one, an FM stereo
broadcast can be viewed as yet another discrete-time sampled
time-division multiplexed, continuous amplitude system.

Yes, I understand this difference. When I use the term quantization I
mean the general process of converting an analog AC signal to a
digital one. This is irrespective of the sampling rate which is driven
by the bandwidth that needs to be quantized.

ALL of these systems are sampled systems, but NONE of them
have quantization. You don't talk about the "bit-depth" of
FM radio (but, you most assuredly could, since their dynamic
range has a bit-depth equivalent).

And ALL of these systems require the SAME constraints as a
classic digital audio system: their input bandwidth MUST be
limited to less than half the sample rate. In the case of
FM stereo, whose effective sample rate is 38 kHz, the bandwidth
of the base channel (which holds the L+R information) and the
subchannel (which holds the L-R information are both limited
to 15 kHz or so.

I also believe that Shannon had some input into the allocation of
bandwidth for FM after the Second World War. as well.

Look at ANY of the data sheets on analog bucket-brigade delay
lines or switched-capacitor filters, they tell you that a low-
pass filter is mandatory to prevent aliasing by the sampling
process.

And NONE of these examples are quantized.

Understood. Like I said, I'm not confused. I was using the term to
describe the digitizing of a finite analog AC signal and was not
confusing quantization with sampling at all. If I expressed that
poorly, then mia culpa, but I was not at all confused when I wrote
it.