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In article <3783@columbia.UUCP> zdenek@heathcliff.columbia.edu.UUCP (Zdenek Radouch) writes:
>>As a practical consideration, all analog signals are band-limited.
>
>False. For a PARTICULAR purpose we can consider property A to be of interest
>only if it is in an interval <x,y>. The property is ANY property, not just
>the frequency - see below!

Sorry, I've been talking like an engineer, not a mathematician.  Sound is
generally bandlimited to 20kHz, video to 4.58MHz; other signals are similarly
band-limited.  Of course, these aren't ideal low-pass filters, to some higher
frequencies do make it through.

>
>>...By the
>>Sampling Theorem, there is a sampling rate at which a bandlimited signal can
>>be perfectly reconstructed.  *Increasing the sampling rate beyond this
>>"Nyquist rate" cannot result in higher fidelity*.
>
>False. ...  Hence the real sampling rate has to be higher than the Nyquist
rate.

Now you've been wearing the engineer's hat, and I the mathematician.
Sure, to account for non-ideal filters, you need to sample above the
Nyquist rate.  What I was trying to say, though, is that beyond a
certain point, increasing the sampling rate of a bandlimited signal
does not increase its fidelity.

>>What can affect the fidelity, however, is the quantization of the samples:
>>the more bits used to represent each sample, the more accurately the signal
>>is represented.
>
>False. Either you are interested in unlimited range i.e. the original analog
>signal, or you assume a particular application and corresponding set of ranges
>of all the properties involved. In the first case (of no practical importance)
>you would need infinite sampling frequency as well as infinite number of the
>bits for each sample. Once you limited the frequency range according to the
>mechanism of hearing you should do the same to the dynamic range.

I guess that's fair.  You characterize the signal by bandwidth and noise,
and that then determines sampling frequency and coarseness of quantization.

There is no such thing as an ideal analog signal.  It will always be somewhat
limited in bandwidth, and corrupted somewhat by noise.

That brings us back to the original question: which representation for
signals is better, analog or digital?

It is my opinion that digital representations are better (could you
tell?).  The reasons?  1) Analog channels introduce dispersion (i.e.
low-pass filtering) and noise.  Digital channels do not affect the
bandwidth of a signal.  Noise (i.e. transmission errors) can be made
virtually nonexistent.

2) Analog processing introduces nonlinearities, dispersion, noise,
intermodulation, crosstalk, and a wealth of other properties whose
parameters are included in stereo component spec sheets.  DIgital
processing is immune to all of these except noise, and noise can be
controlled with a proper numerical analysis.  Additionally, exotic
nonlinear processing is easy to do digitally, where it may be
impossible to do via analog.
-- 
Ken Turkowski @ Apple Computer, Inc., Cupertino, CA
UUCP: {sun,nsc}!apple!turk
CSNET: turk@Apple.CSNET
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