Re: anti-aliasing
- From: Robert Baer <robertbaer@xxxxxxxxxxxx>
- Date: Sun, 25 Nov 2007 19:47:30 -0800
John Larkin wrote:
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.
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
Possible solution: trigger start and stop of sample period from incoming signal, say at zero crossing + slope.
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.
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.
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.
Ratio? Maybe 11.5 if free-running (both stable, temp comp), possibly to 31.5 (maybe more) if clocks generated from same crystal.
.
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