anti-aliasing

Randomly varying the sample points will randomly vary any aliasing going on, which means that instead of having a few really bad magic frequencies you'll have only slightly bad, but broad magic frequency ranges -- just how broad and how bad would depend on your sampling, and could either be found by analysis or simulation.

If you couldn't live with the resulting error, sampling at two distinctly different rates, overlapped, then checking for one of the set of samples being aliased to DC may be more effective. The algorithm, however, would be way more complex.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
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If the granularity of your "pseudo-random delay" is small enough, and you take enough samples, then the answer will converge on the correct one (i.e. no effects of aliasing will be seen).

How many samples to take as a function of delay granularity to give an acceptable amount of error? That's the hard part.

You should probably repost on comp.dsp, or go to comp.arch.fpga and ask for Ray Andraka's help. He's smarter than everyone here -- combined!

Bob

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. 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.

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.

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

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.

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.

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

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

I think you might be going about it the wrong way.

The DC terms are simply the integrals of the function.

i.e., for a signal f(t)

DC term = F(0) = int(f(t)) abs DC term = G(0) = int(|f(t)|)

If you cannot take the abs of a signal(by using rectification say, then you can also do it by clipping.

F(0) + G(0) = int(f+(t))

where f+(t) is the positive terms of f(t)(which can be simply gotten by rectification) and F(0) is simply determined by an integrator.

Seems like you can do all the hard work using an op amp or two and your adc will simply digitize the result.

This even goes along the line that you should just LP your signal because they do not effect the DC term. LP it enough so that your sample rate is 2x the highest frequency. (I suppose there is an issue of practicality here if your sample rate is extremely low... in that case just get a faster adc.)

If you check the number of times each ADC output showed up - creating a histogram - you could probably see when you were sampling at some multiple or sub-multiple of the sampling frequency.

Enough completely random samples would give you an M-shaped histogram, with every voltage interval between the peak and the minimum of the sine wave eventually getting some hits. If your sampling is synchronous (sampling at an exact multiple of the sine-wave frequency or some integral fraction of the frequency), you won't get this pattern, but will rather see a number of isolated peaks in the histogram where the sampling hits at more or less the same phase time after time.

If your sine wave amplitude could go to down to zero you wouldn't be able to distinguish the single peak you'd see on the histogram from the single peak that you'd get from perfectly synchronous sampling at the same phase point, but you could check that by changing the sampling frequency.

You haven't given enough detail for me to be sure that is would be a practical approach, but it might give you what you seem to want.

-- Bill Sloman, Nijmegen

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(.)? Is there any analytical basis for this that you actually understand? What range of confidence are you looking for? 75%? 90%?

99.9%? or what? Give us some numbers. 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.

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...

This will dither the error through the whole range. Although you will avoid the worst cases, the average error will be higher.

I would lock the sampling to the incoming frequency. That can be done either by adjusting the sample rate directly or by resampling in the software.

Vladimir Vassilevsky DSP and Mixed Signal Design Consultant

I'm pretty sure it is just a simplified version of sequential particle filtering, and very simplified if he knows the input is sine, there are no guesses about the form of the distribution whatsoever.

Right. It's sorta like a delta-sigma dac, where artifacts are pulverized and scattered to become a broadband noise floor.

As I mentioned, the incoming frequency is unknown. I'm perfectly willing to take, say, 1000 samples to get, say, 2% measurement accuracy, if I can ensure that my sampling can't alias the sinewave input. One of the checks I'm making on sinewave quality, and on the signal chain producing it, is that there is actually a very small DC offset. I'm not willing to run a bunch of trial runs and pick the best one by some as-yet-unknown criterion; the BIST function I'm running already takes 7 seconds to execute.

I was just wondering if the problem has come up before, and if anyone had ideas or algorithms for sample time splattering that guaranteed no aliasing.

John

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

Certainly.

What range of confidence are you looking for? 75%? 90%?

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

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

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

--
What\'s the input frequency range and, if you can vary the sample
rate, what\'s the maximum rate?

-- snip --

This should work. The added delays wouldn't have to be Gaussian, you'd just want their spectrum to be fairly white.

As I pointed out in my response to your original post, though, this will practically guarantee you some DC noise floor.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html

Ooh. Testy.

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.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html

Another approach would be to do it twice, with sampling rate F and F(1+1/N), where N is the number of samples. The lowest frequency that aliases both of those to DC is (N+1)*F. If you use three frequencies that are relatively prime, it'll be N**2 * F, which should be enough to cover most uses. This has the advantage of relying only on theory you can do in your sleep, which is important for a BIST routine.

Cheers,

Phil Hobbs

Well if your system is generating the sine wave then how does it come to pass that you don't know the frequency? If you're admitting the possibility of a harmonic or subharmonic output, what makes you think it will even be constant or a sine. You may need some analog to steer your processing in the large...like a filter bank or a voltage controlled variable center frequency band pass or something or IF swept mixer thing, dunno.

-mystified

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.

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

Say, 2 KHz to 1 MHz. The flat-out sample rate is 12.4 KHz (software loop, bit-banging a 12-bit serial ADC) which I can slow down on a per-sample basis, randomly or swept or whatever. I usually take about

1000 samples and average the mean and the software-rectified mean.

John

For N=1000, (1+1/N) is only 1.001. That won't move an alias very far. The alias doesn't have to be to DC to mess me up, it just has to be to a low frequency relative to my total sampling run duration.

If I did it twice, which measurement would I trust? Not the one with the lowest DC offset, because I'm trying to measure offset.

Even three runs (which would take a lot of time) would be tricky... would I throw out the one that has the highest DC offset, and average the other two? Or pick the two that agree best?

Too much work!

John