Archived from groups: rec.audio.tech (
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Joe Kesselman wrote:
> Tim Martin wrote:
> > That is, for any method of storing an analog signal in x bits, it
> > is possible to devise a digital storage mechanism using >x bits
> > which can be used to reproduce a more accurate rendition of the
> > original analog signal.
>
> Well, yes, analog is _theoretically_ infinite precision.
No, it is not, not even theoretically.
Because for there to be infinite resolution for any arbitrary
signal, even in theory, there must be infinite signal-to-noise,
because the presence of noise limits the resolution of the signal
to a level of ambiguity defined by the level of the noise. And since
no noise requires that the system operate at a teemperature of
precisely 0 degrees K, the introduction of ANY signal into such
a system will be the equivalent of raising itsd temperature and in
and of itself introduces noise. SO that shifts the requirement to
having a finite noise floor. And a finite noise floor, even one
which is vanishngly small, requires that to achieve the infinite
dynamic range that is intrinsic of infinite resolution requires
signals of infinite amplitude, which means infinite energy.
And even if we ignore all that, we're bitten by the fact of simple
quantum uncertainty, which prevents perfect knowledge of a system.
And further, to have infinite resolution in the time domain requires
the system to have infinite bandwidth. Since bandwidth and time are
related by the fundamental time-frequency uncertainty relationship,
the only way to have infinite resolution in the time domain, i.e.,
the ability to distinguish to event separated by infinitesimal time,
the system must exist for infinite time.
And the assertion that analog has infinite time resolution means
that ANY change in level in a an infintiesimal period of time
intrinisically requires infinite energy.
So, no even THEORETICALLY, analog does not, indeed, CANNOT have
infinite resolution. To claim so is absurd.
> ... but for most practical purposes, "good enough" really is Good
> Enough. Human hearing is not infinitely accurate. Nor is any real-world
> recording medium.
Or even a theoretical one.
> Digital beats the accuracy of most analog media quite handily, given a
> suprisingly small investment. The limiting factor, actually, tends to be
> the analog hardware used to get the signal into and out of digital form.
Indeed, this is often the case.
And, as Shannon quite rigorously demonstrated over half a century ago,
any system sampling at more than twice the bandwidth of the signal
and simply having sufficient bits (dynamic range in dB/6.02 db/bit)
WILL encode that signal with perfect accuracy. Increasing the sample
rate or the bit depth WILL not result in ANY more accuracy, just a
waste
of data bandwidth.
/mindspring.com/~benbradley
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