On Mon, 07 Mar 2005 08:11:00 GMT, "audiodir"
wrote:

I have no doubt as to the Fourier statements and theory, but that is also
based on unlimited data. It would seem that in the case where there is an
upper limit, then the data available becomes truncated as you approach that
limit, making recreation of a waveform much more difficult.
Perhaps the problem is not so much with the Nyquist theory as its
application. After all, a DAC has to set the parameters of what waveform it
seeks to recreate. I believe the Spectral DAC had an option to set different
algorithms to use in the decoding process. The waveforms generated are not
dissimilar to the differences seen in a cadcam system when asked to
interpolate a curve over various points.

Different situation entirely. The whole point of Nyquist/Shannon is
that, if you have only two sampled points of reference, i.e. if the
samples are of a signal having a frequency between one-half and
one-third of the sampling rate, and if you *know* that the input
signal is bandlimited to less than half the sampling frequency, then
only *one* possible curve will fit the two points - it is a sine wave
of a specific frequency and amplitude.

If the curve were *not* a sine wave, then it would *by definition*
contain harmonic content, and hence would *not* be band-limited to
less than half the sampling frequency. This causes an effect known as
aliasing, which is a *distortion* which does not exist in a properly
implemented sampling system.

It is true that the Spectral and several other DACs (also some Wadia,
Pioneer and Sony CD players), did indeed use reconstruction filters
which allowed out of band products to appear at the output. This false
imaging is a *distortion*, in other words it's a bug, not a feature.
Heck, some loonytunes 'high end' players from the like of YBA and
Audio Note, don't even *have* a reconstruction filter, they just let
*all* the rubbish out!

While most music is a series of sine waves,

Actually, *all* bandwidth-limited signals can be represented as a
series of sine waves.

there are a lot of impulses and
other unusual waveforms (think of the 'grundge' associated with rock
electric guitars and the inherent distortion those instruments can produce).

What *appear* to be impulses, certainly have finite leading edges, and
can threfore be represented by a series of sine waves - even if you
need to up the sampling rate to capture anything higher than 22kHz.
But why would you want to, unless you are a cat or a bat?

BTW, the 'grunge' associated with a heavily distorted electric guitar
is all below 10kHz, so no problems capturing it.

No wonder that the classical community was the first to embrace CD. I know
many rockers that even today claim that analog captures the guitar sound
more accurately.

People make all kinds of crazy claims - and would *you* take the word
of someone who's spent the last decade with his ears three feet from a
Marshall stack - and his nose in a snowdrift? :-)

I believe the Synclavier uses a sampling frequency of 100kHz. If it needs
that much to create a specific sound, how can a lowly 44.1 kHz sampling rate
reveal the subtleties that a programmer/musician may want to play.

Who says that the Synclavier *needs* a 100k sampling rate? With modern
kit, 24/96 sampling is trivially easy (and cheap) to do, but it's very
arguable that it's *necessary* for 'perfect sound'. You probably have
a 24/96 soundcard in your PC, but do you *need* 96k sampling?

At any rate, to continue this discussion is fruitless for me. There are
limitations, and whether one can hear it or not is a subjective thing.
Different people are sensitive to different things, but of course your own
personal sensitivities are all that counts.

And not one single person has yet been found who can reliably and
repeatably tell the difference between 44.1k and 96k sampling, when
they don't *know* which is playing.
--

Stewart Pinkerton | Music is Art - Audio is Engineering