[ARSCLIST] The circle analogy (was: Is recording to Reel-to-reel still the preferred preservation method?)

[Jon Noring <jon@xxxxxxxxxxx>]

Don Cox wrote:
> Parker Dinkins wrote:

>> At least one study has shown that using a sample rate above 96kHz
>> provides no benefit when used with well designed filtering, and in
>> fact using 192 kHz results in reduced accuracy as well as unnecessary
>> additional expense, both in storage and equipment requirements. See
>> Dan Lavry's white paper on this topic at
>>
>> http://lavryengineering.com/documents/Sampling_Theory.pdf

> It would probably be possible to "prove" that a 10x8 photograph is no
> better than a 5x4 photograph. But it is.

I assume what you mean is that an image file with twice the linear
resolution (pixels per inch) compared to another image file of the
same picture will look sharper. Up to a point this is true (until we
get to very high linear resolution where we run up to the limits of
human vision and we won't see any differences -- it's hard to
discern between 1200 ppi and 2400 ppi, for example, while the
difference between 100 ppi and 200 ppi is very apparent.)

It is sort of a mystery to many why digital audio works as it does.
One reason it works as it does is that the samples represent a sum
of "periodic signals", and this added bit of information is critical
to understand why one only needs to sample (theoretically at least) at
twice the frequency of the highest frequency component in the signal
(Nyquist). If we did not have this added bit of information, the
samples can represent an infinity of possible curves (including
connecting each successive sample with a straight line.)

Let me give an example. Did you know that to perfectly represent any
circle we only need three points -- that we do not need to sample a
huge number of points on the circle so as to later reconstruct it? The
key to this is that in addition to specifying the location of the
three points we also specify the nature of the curve which contains
those three points. In this case we simply say "these three points
represent a circle." It is obvious that if we fail to say what kind of
curve contains the three points that we'd have an infinity of possible
curves to choose from (the simplest being a triangle.)

Thus, the key to understanding digital audio is that the linear
parade of samples represents a periodic signal. Stating "periodic
signal" is the added bit of information, just like we must say from
the above example the nature of the curve which fits the three
points (e.g., "these three points represent a circle".)

Jon Noring
Sound Preserve/Project Gramophone