Re: Tom Scholz on Why Digital Sucks ... again
- From: Ben Bradley <ben_nospam_bradley@xxxxxxxxxxxxxxx>
- Date: Fri, 22 Aug 2008 13:22:40 -0400
On Fri, 22 Aug 2008 13:23:48 +0200, "Meindert Sprang"
<ms@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
"Chel van Gennip" <chel-news@xxxxxxxxxxxx> wrote in message
news:6h7gj5Fjp9k3U1@xxxxxxxxxxxxxxxxxxxxx
You should either study the theory, do the tests,
When I generate a waveform in Audacity with a frequency of 11020Hz at a
sampling frequency of 44100Hz, I can see the AM modulation on my screen. I
Scott's post told me what you're seeing, and indeed what's shown on
the screen is often NOT the same as what gets sent to or what comes
out of the A/D converter. I've used audacity, but not for zooming in
time-wise on waveforms, so I don't know how it handles drawing
individual waves, but maybe you can do the following with it.
I just did this in Cool Edit 2000. Viewing 77mS or greater on the
screen shows this "amplitude modulation," and indeed the points
available for the waveform do indeed cause the peak-displaying
software (it displays the peaks of the SAMPLES, not of the waveform)
at that zoom range to show a solid "carrier" waveform that appears to
be modulated by a full-wave rectified sine wave.
But zooming in shows the real story. There are (approximately, but
very close to) four sampling points for each cycle of the waveform,
and they vary slightly in phase from one cycle to the next. If you
zoom in to display about 1mS of the waveform, you'll see these four
points on a sine wave - I don't know if CE's display software uses a
low-pass filter or what to draw the waveform from the points, but it
appears to show the analog representation of those four points, which
happens to be a sine wave. If you go pan around you can see the points
at various places on the waveform (there may be two near zero-crossing
and one each near the positive and negative peaks, or they may be all
the same moderate amplitude + and -, starting at about 45 degrees into
the waveform), but regardless of where they are, they all add up to a
sine wave with the correct phase and amplitude. Zooming back out a bit
to show 17mS on the screen, there are many sine waves with irregular
peaks, but this is because of the software not having enough points to
correctly show enough of each sine wave - sometimes a peak lands on a
screen pixel, and sometimes not.
I'd do a screen shot and put it in a webpage to show you, but I
just remembered this has (amazingly!) already been done. There's a
free book on digital signal processing available online here:
http://www.dspguide.com
Look at the chapter on the Sampling Theorem here:
http://www.dspguide.com/ch3/2.htm
and look at figure 3, especially diagram c showing a sampled sine wave
of 0.31 times the sampling rate. And be sure to read the caption for
the diagram that starts with "Proper and improper sampling," it
mentions how those odd looking sample points all indicate points on
the same sine wave.
am now going to hook up my scope to see what is left of that after
conversion to analog.
The output (or "reconstruction" - sorry, Mr. Sommerwerck) filter is
what converts those 'sample points' to the original sine wave (the
intended output as shown in the figure, diagrams a through c, or an
unintended one as shown in d).
Meindert
.
- References:
- Tom Scholz on Why Digital Sucks ... again
- From: James Price
- Re: Tom Scholz on Why Digital Sucks ... again
- From: Meindert Sprang
- Tom Scholz on Why Digital Sucks ... again
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