Always good to have a nice interaction about the theoretical basis of
scientific work, and related practical implementations, isn't it ?
TO add a little positive note to the whole story, after maybe having
bashed some peoples' work in a "theoretically limited" corner too much
for their immediate liking, a little (and partial) explanation of the
subjects I've been working on, in the context of exactly the music
related signal processing I think is the honorable thing to work on in
this context.
First, the sampling error issue in many cases can have an easy solution,
if you take it that nothing much thus far is perfect, and thus a
solution is "only" an iteration with better accuracy: higher the
sampling frequency, make sure your vertical (quantization error)
resolution in the intermediate result computations is sufficient, and
your results are going to become more accurate, pretty much in general.
Second, there are various ways to deal with the making and producing of
digital signals that improve the possibility of getting the final result
true to nature. For instance to get natural e-powers in the samples
signal that are pretty correct, use a quality analog equalizer, and
properly sample the the output of it, that will put the right impulse
response in the sample. And the advantage of doing that all with high
quality is: the resulting samples can be "perfectly reconstructed", or
seriously and with high quality (== much processor burden) upsampled,
which is a partial reconstruction. I favor the idea of making a sample
stream either intended for some sort of DA convertor (most DA convertors
are in only a few groups of reconstruction filter kind, and a in that
group are at least alike), or intended to act as reasonably perfect
samples, as in that up-sampling or a serious attempt to do perfect
reconstruction will not fail. My practical experience is that this all
can work fine, but of course it becomes a more prevalent issue that all
kinds of digital filter (and other types of processing, including
non-linear and harmonics inducing) we've gotten accustomed to use,
aren't (yet ?) very perfect.
Third, as it is my perception that it has been going on for a very long
time in the A-grade (studio ) materials, it is reasonable to search for
certain signal properties that aren't much in the sampling error range,
and that have musical meaning. Taking a medium short signal convolution
as a starting point, it is possible to detect, and in some cases to
free, various obvious and less obvious constantly present imperfections,
and by dynamically working with certain averaged sub-bands (as I've done
work with) musical, acoustic, and sampling error dissociating
improvements can be achieved.
T.V.
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