Re: anti-aliasing

On Sun, 25 Nov 2007 19:47:30 -0800, Robert Baer
<robertbaer@xxxxxxxxxxxx> wrote:

John Larkin wrote:


Suppose one (actually, me) were firing an adc at some fixed rate,
ballpark 12 KHz in this case, and the input to the adc was a sine wave
of fixed but unknown frequency. The adc will take a bunch of samples,
ballpark 1000 maybe, and I want to compute the mean (ie, dc value) and
the mean of the abs value of the samples (ie, the ac value). That
works, but sometimes the input frequency aliases against the sample
rate and messes up the data, like gives a big average dc value when
there's really none there.

(This is not a Nyquist issue; the sample rate may be above or below
the sinewave frequency.)

So maybe I can fuzz up the sample rate so that it can't alias against
any constant sinewave frequency.

I could add a pseudo-random delay after every adc sample shot; but the
mean sample rate wouldn't change a lot. Or I could add successive
delays, essentially sweeping the sample rate down.

Any ideas?

John

Issue #1: What time period is going to be used for the sampling? If
the (presumedly) sine wave is of a sufficently low frequency WRT to full
sample time, then any given sub-section of that sine would be samples,
giving obvious errors.

That's a separate issue. Obviously I need to sample for many cycles of
any waveform, to avoid getting just a slice. Let's assume I'll sample
for long enough to avoid that problem.

Possible solution: trigger start and stop of sample period from
incoming signal, say at zero crossing + slope.

Can't do that; my sample rate is generated in software and I have no
trigger hardware.

If it is a complex waveform signal, that might not be a useable solution.
Issue #2: if the input waveform is fast enough, the samples will
(again) represent only a small time section of the presumedly repeating
waveform, with the same obvious errors.

I don't understand that one. If the signal rate is well above the
sample rate, I'll be sampling over many cycles, so the only problem is
down-aliasing.

In either case, "small" dithering of the sampling periodicity will
not help; it might be useful when the input periodocity is near one of
the harmonics of the sampling rate.
For kicks, assume the nominal periods are the same; dithering would
only allow one to "slip" left ot right of the assumed synch point,
again achieving only part of the full waveform.
Hell, ASS-u-ME the sampling rate is *exactly* twice the input
waveform rate; i ask you the following nasty question: is it possible to
recover the input waveform? The answer might make one think that
Nyquist was a liar.

I'm not trying to recover the waveform. All I want to do is measure
its mean and the mean of its abs value.

In the 2:1 case, I'd always get a mean of zero, and an AC value (mean
of abs) that depends on the relative phases for that particular run.


So.
If it is a given that the input frequency is unknown and possibly
wideband, then use two samplers, where the rates are decidedly NOT
harmonically related; maybe one sampling for a long time to recover low
frequency waveforms, and the other some generic high speed sampler for
comparison purposes.

Sorry, I only have one adc. But if they differed, which one would you
pick to believe?

Ratio? Maybe 11.5 if free-running (both stable, temp comp), possibly
to 31.5 (maybe more) if clocks generated from same crystal.


I'm thinking that if I add a pseudorandom delay after each sample, so
that the sample period varies from the original to, say, twice as
much, the spectrum of the sampling impulses will be spread over about
a 2:1 range, so nothing can alias against it. It's a little easier to
think about if the added delays had a gaussian distribution, but
uniform might be OK too.

John

.

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