23 Nov
2015
23 Nov
'15
11:28 p.m.
This is just wrong. I wish you would pay more attention to what you don't
know than what you do know.
You are mssing several key things:
1) all waveforms can be represented as the sum of a series of sinusoids.
The more sinusoids in the series, the more accurate the model of the
original waveform (even if it was not composed of any sinusoids to begin
with. This is the basis of both Fourier analysis and Fourier synthesis,
which are key concepts in the abstract representation of wave data. There
are a few complications with this model, but for the purposes we are
discussing here, it is 100% complete and accurate.
2) Nyquist's theorem proves (and note that I said *proves*, not
"asserts") that sampling at a given sample rate provides enough data to
reconstruct **PERFECTLY** any signal made up frequencies up to the sample
rate divided by two.
2) the interpolation done by digital-to-anlog converters is based on a
combination of points (1) and (2), and results in **PERFECT** reproduction
of the original waveform (if (and only) the clocking is identical). In
reality, there is no "low-res". See Monty's example of 8kHz sampling rate
in the video.
Your comparisons with letter shapes is actually somewhat apropos, but only
for letter shapes formed by band-limited waveforms. You can, in fact,
synthesize letter shapes (or any other shapes) using fourier synthesis, but
it is slow and generally not how typography works. If you do know how it
actually works (e.g. the specific spline algorithms that will be used by a
font renderer) then you can, in fact perfectly "sample" a font with a
handful of points per letter that will feed the spline rendering algorithm.
The data is generally called a TTF (TrueType Font) file, and is used by
your computer all the time.
Speculating on interesting ways to abuse/use points (1), (2) and (3) has
been a rich source of ideas for audio engineering and processing for about
a hundred years. It doesn't do a lot, however, to carry out this
speculation without a basic background in signal processing in general and
digital signal processing in particular.
On Mon, Nov 23, 2015 at 4:15 PM, jonetsu(a)teksavvy.com <jonetsu(a)teksavvy.com>
wrote:
On Mon, 23 Nov 2015 16:02:40 -0500
"jonetsu(a)teksavvy.com" <jonetsu(a)teksavvy.com> wrote:
I have replied an hour ago, but the reply did not
make it yet. Maybe
due to the 48K attachment. So let's try with a low-res one :)
As the low-res version of the drawing may induce, reconstructing the
original does not seem too hard. You have to know how the letters
of the alphabet of that type of font are, and a few details about
shapes so it is possible for the algorithm to reconstruct the tip of
the arrow. And then based on this to exclude all other noise. Not too
complicated.
Then for audio it would be possible. Simply enter the parameters.
Martin guitar (model type) made in summer of 1994, brand new nanoweb
strings, Dunlop flat pick .73 mm, velocity, and a few other parameters
(using Finger Ease spray or not). Then feed a coarse wave shape and
voila, you get a rich Martin 440Hz (precisely :) 5th string output. :)
The possible technology is interesting, though.
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