Robert:
Right, I think the debate over 40 kHz signals and whether or not they have
any effect on us at all is cool, but not what I wanted to ask.
I'm more concerned with how good 3 samples is at 15 kHz, which I can hear,
albeit weaker every year.
So, 3 points in time, separated by 1/44,100 of a second, with 15 bits of
resolution (plus the polarity bit). Can this really define any sine wave
accurately? What about a decaying sine wave, one who's amplitude is
decreasing linearly or logarithmically with time? Can a mere 3 points
really stay true to this, even without getting into discusisons of linearity
of a DAC at -90 db.
This is my real interest in high frequency recordings. I don't intend to go
out and buy a super tweeter.
Thanks!
Erik
"Robert Morein" wrote in message
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"Arny Krueger" wrote in message
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"ScottW" wrote in message
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"Erik Squires" wrote in message
ervers.com...
So, here's my question. If I digitize a 15 kHz signal, using a 44.1
kHz sampling rate, I'm going to get about 3 samples / cycle.
Are the normal digital filters good enough to reproduce a 15 kHz
singal with varying amplitude?
Deconstruct this signal to frequency domain and it won't be a pure
15 kHz.
Wrong.
There has to be another component imposed on the 15 kHz that "varies
the
amplitude".
Wrong.
Three samples is sufficient to define a sine wave that has unique
frequency,
phase and amplitude. In fact, just slightly more than two samples is
sufficient.
Wrong.
Arny is simplistically parroting the Nyquist Theorem, which states that
any
signal can be reconstructed with a sampling rate twice the maximum
frequency
present in the signal.
This, however, is a theoretical result. It is impossible to implement in
practice, because the analog reconstruction filter required would have to
cut off instantaneously at 15kHz. Since it can't, the result would be a 15
kHz signal with higher harmonics
To understand what happens if the reconstruction filter is not present, 2X
sampling would provide a simple 15 khz square wave. To the extent that the
square wave is not brick wall, some of the harmonic structure of the
corresponding square wave will be present.
In theory, using noncausal filtering, it's possible to make the brick wall
filter. In practice, it can't be done.
One of the original innovations in CD DACs was the oversampling DAC. In
this
approach, the signal is interpolated using a digital filter chip. It is a
form of upsampling. The upsampled signal is easier to filter.
Unfortunately, the implementation of digital interpolation algorithms
remains to this day an incompletely solved problem.
Recently, Arny brought forth a recent AES paper that purported to show
that
signals above 20 kHz make no difference in the perceived quality of the
reproduction. There is a considerable body of evidence that the ear can't
hear above 20 kHz, yet many listeners report improved fidelity with higher
sampling rates and greater bit depth. The most probable explanation of
this
lies with the reduced phase of enhanced/upsampled/high bit rate systems
shift at frequencies approaching 20 kHz.