[William Sommerwerck]

When Hemo (Marvin Miller) insists that Dr. Science (Dr. Frank Baxter)
respond with the two words that shows he understands the essence of blood,
Dr. Science comes back with "sea water".

So... Here's my equivalent of the "sea water" answer.


"Is the audio output of a CD player analog or digital?"

It's digital. Once you've converted analog to digital, the damage is done
and can't be undone. You can't go home again. Here's the explanation...

Consider the classic sampling of a band-limited signal. The sampling process
produces a string of pulses whose amplitudes are exactly the amplitude of
the signal at the instant of sampling. Because this amplitude can vary
continuously (ie, have any value, without restriction), the pulse chain is
an analog signal. (analog = data representation by continuously variable
values)

Fourier analysis shows that the pulse train contains the original signal,
unmodified. If we play the pulse train through a system free of
intermodulation distortion, we will hear the original signal, unchanged. *
This is true even if the system has "infinite" bandwidth, because the
original signal is a component of the pulse train; no filtering is required
to "recreate" it.

To convert this pulse train to a digital signal, we first have to quantize
its level. (I'm ignoring the use of dither, to clarify the point I'll be
making. We'll consider it later.) In a 16-bit system, the signal's original
amplitude range would have to be divided into 65536 equally spaced levels.
**

Once the quantization is performed, the signal is digital. (digital = data
representation by quantized values) Any sample can have an amplitude of only
one of 65536 values. Each of these represents a "number", as assuredly as
the bit settings in a two-byte register represent a "number". ("12345" is
not a number; it is the representation of a number.)

If you don't believe that (and of course, you don't), imagine that you had
hundreds of sheets of paper with lines whose lengths were directly
proportional to the quantized amplitudes, with the relative length printed
next to each line. If I said I would send you the number of my street
address, and you opened the envelope and found a paper with a long line on
it, would you have any trouble finding the line of the matching length on
the reference sheets, and determining that my condo number was 17610? I
don't think so.

Let's repeat the listening test. If the quantized samples are played, we'll
hear the original signal, with varying amounts of quantization noise. ***
Furthermore, if we converted the quantized levels to digital numbers, then
reversed the process, converting those numbers back to the corresponding
voltage levels, the quantization noise would still be present. In other
words, there's no way to audibly distinguish a quantized pulse train with
the same signal recreated from a string of "numbers" -- because there isn't
any difference. The level-quantized samples and the PCM bit sequences
representing them are /exactly the same numbers/.

"But wait!" you say. "If you run the signal through a low-pass
reconstruction filter" (which doesn't and never will exist, but we'll ignore
that), "all them sharp little edges will be rounded off, and the horizontal
lines will be tilted and curved, and we'll have a nice analog signal again.
Right?"

Wrong. The signal still contains the quantization errors, because they
appear in the "baseband" component of the signal, and cannot be removed by
filtering.

So... How can a signal with quantization noise can be analog? (I'm waiting,
Hemo.) It can't, of course.

Regardless of what the waveform /looks like/, the fact is that it comprises
only a finite number of signal levels. If it didn't, there wouldn't be any
quantization noise.

QED. The output of a CD player is digital, not analog.

As for dither... It randomizes the quantization noise to minimize its
audibility. But the noise is still present, because the signal does not vary
in a continuous fashion. It's just that the errors have been moved around to
reduce their correlation with the signal.


* Other than the frequency response variation caused by the finite sampling
width.

** One could have non-linear quantization. I'm ignoring that for simplicity,
and because it's not often done.

*** If you don't have a test CD with an undithered tone sweep, find one.
It's quite interesting to hear the bursts of quantization noise as the test
tone sweeps through frequencies that are submultiples of the sampling rate.
Of course, there's quantization noise at _all_ frequencies. It's just that,
when the test tone is not "too close" to a submultiple, the errors are
sufficiently "random", particularly with musical material, not to be
particularly noticeable at normal listening levels.