Re: anti-aliasing

On Mon, 26 Nov 2007 09:17:00 -0800, Tim Wescott <tim@xxxxxxxxxxxxxxxx>
wrote:

John Larkin wrote:
On Mon, 26 Nov 2007 09:33:28 -0500, Fred Bloggs <nospam@xxxxxxxxxx>
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.
Do you intend on using a sample zero mean, or closeness to it, as a
numerical criterion for confidence in the estimate of the mean of
abs(.)?

This is a BIST (self-test) function for a DDS synthesizer. Any
significant mean value would be an indicator that something is wrong
in the stuff that generates the sinewaves. That might be excess dc
offset, clipping, or distortion.


Is there any analytical basis for this that you actually
understand?

Certainly.

What range of confidence are you looking for? 75%? 90%?
99.9%? or what? Give us some numbers.

I'd like to verify that the sinewave amplitude is within, say, 2% of
my target (that's the system spec) and that a 20 volt p-p sine has
below, say, 200 mV of offset. If I don't have aliasing, I'm seeing
offset measurements in the 50 mV range. The BIST subsystem is pretty
simple: a relay diverts the signal from the customer connector into a
12-bit ADC, and the rest is all firmware, including the ADC triggers.


There is a form of filtering
derived from principles of artificial intelligence that is more or less
applicable, it is called _____ _____ filtering and it's quite powerful.

There's no filtering that can remove aliases once they're in the data.

Any ideas?
The very word "ideas" in this context actually means "guesses." That
would be in keeping with your methodology. The success rate will be a
function of something called the density of useful solutions...

Where do you think new concepts come from? They come from generating a
great number of ideas, and riffs on those ideas, and filtering them
for quality. A filter with no input has no output.

I wouldn't expect ideas from you, because you are hostile to the
chaotic nature of the creative process. Some people are that way, and
can do good work in other ways, but they won't allow themselves to
design.

John


Ooh. Testy.

Well, Fred keeps insulting me because I have ideas and design things.
He seems to think that the initial stages of a design, the explore
possibilities phase, is impure and beneath his dignity.

I've known lots of people who couldn't design because they feel
insecure in the early stages, the deliberate uncertainty phase. These
people, if thet are responsible for design (which they shouldn't be)
tend to look for well-analyzed prior art, and if they can't find any,
usually seize onto the first clumsy concept they can come up with, and
then settle into brute-force analysis and implementation of a bad
idea. Design is a creative, chaotic, psychological process that
uptight people don't like and seldom respect.



Do you get to know what frequency the DDS is running at? If so, you
could adjust your sampling rate to match, so you got a good picture of
what it was doing. If the DDS always went fast enough, and the ADC
sample time could be set precisely enough, you could even build up
exactly one cycle of the output and analyze it for a heck of a lot more
than just DC content.


When I run autonomous BIST, I test a range of frequencies. I suppose I
could fine-tune the sample rate, or the test frequencies, on a
case-by-case basis, or do more number crunching and find one magical
sample rate that won't alias *any* of my test frequencies. But there's
another mode where the customer can program a waveform and ask for it
to be measured (which we also use in testing) so it would be cool to
have a general solution.

John

.

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