On Mon, 23 Nov 2015 17:28:02 -0500
Paul Davis <paul@email-addr-hidden> wrote:
> 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.
Ah. This is actually quite an important notion.
> 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.
I'll look up these two.
One thing that is clear, and this what got me thinking that way, is
that in Audacity, when zooming is done to see the actual sampling
points on a wave from a human voice sound, the line between two
sampling points is straight. Now, with thousands of sampling points a
curve can be represented if one zooms out enough to see it as a curve.
Although this level of detail, to examine straight lines between two
sampling points, might very well be in practical terms /not/ useful
since it foregoes meta-notions such as 1) and 2) which are more
important in day-to-day applications.
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Received on Tue Nov 24 20:15:01 2015
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