Well, bandlimited to a bandwidth fs/2 (but the distinction isn't
useful for audio), and given perfect reconstruction circuitry. But as
far as I can gather, Theo's concern is what happens when, as is
inevitable in practice, the reconstruction circuitry is imperfect?
And that is an interesting question, academically speaking, if there
really isn't a body of theory to cover reconstructive imperfection -
if only to be certain that all the improvements made to DAC technology
in the last three decades have actually been _improvements_.
But I think all of this is probably covered by existing research
anyway. Minimising phase disruption in digital filters is well
understood; LSB errors and resistor chain nonlinearities are fairly
obvious, sources of relatively predictable badness, and can be
assessed in the same way as nonlinearity in general; clock jitter is
easy to simulate... and then there are analogue reconstruction
filters. Unless I've missed any, I don't think there's anything else
to look at, unless he wants to disprove or augment Nyquist-Shannon.
Which would be an achievement, true, but... I would humbly submit that
there might be more fruitful avenues towards seeing Verelst theorem
in the indices of 22nd-century audio textbooks.
Still, I understand great white whales all too well; and if Theo
_needs_ to harpoon this one, we should perhaps not stand in his way.
On 05/06/2015, Stefan Stenzel stefan.sten...@waldorfmusic.de wrote:
Theo,
Any continuous function bandlimited to frequencies fs/2 is completely
determined by its samples.
That’s the essence of the sampling theorem, which answers all your
questions.
Stefan
On 03 Jun 2015, at 22:47 , Theo Verelst theo...@theover.org wrote:
Hi,
Playing with analog and digital processing, I came to the conclusion I'd
like to contemplate about certain digital signal processing
considerations, I'm sure have been in the minds of pioneering people quite
a while ago, concerning let's say how accurate theoretically and
practically all kinds of basic DSP subjects really are.
For instance, I care about what happens with a perfect sine wave getting
either digitized or mathematically and with an accurate computer program
put into a sequence of signal samples. When a close to perfect sample
(in the sense of a list of signal samples) gets played over a Digital to
Analog Converter, how perfect is the analog signal getting out of there?
And if it isn't all perfect, where are the errors?
As a very crude thinking example, suppose a square wave oscillator like in
a synthesizer or an electronic circuit test generator is creating a near
perfect square wave, and it is also digitized or an attempt is made in
software to somehow turn the two voltages of the square wave into samples.
Maybe a more reasonable idea is to take into account what a DAC will do
with the signal represented in the samples that are taken as music,
speech, a musical instrument's tones, or sound effects. For instance, what
does the digital reconstruction window and the build in oversampling
make of a exponential curve (like the part of an envelope could easily be)
with it's given (usually FIR) filter length.
In that context, you could wonder what happens if we shift a given
exponential signal (or signal component) by half a sample ? Add to the
consideration that a function a*exp(b*x+c) defines a unique function for
each a,b and c.
Anyone here think and/or work on these kinds of subjects, I'd like to
hear. (I think it's an interesting subject, so I'm serious about it)
T. Verelst
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