Bandpass subsampling?

There is a need to estimate power which falls into given wide (~30% of 
Nyquist) bandwidth. Power spectrum doesn't matter; just overall number. 
The power estimate is not needed often; so a decimation factor of ~1000 
is preferred.

Straightforward way would be make FIR filter to cut out the bandwidth, 
run this filter at every 1000th sample, then measure power.
But if the input is periodic or near periodic to decimated sample rate, 
then the power output would oscillate with difference frequency. This 
corresponds to comb response in spectral domain; ideally there should be 
flat response.

Is there an efficient way to deal with this problem?
I am thinking of dithering decimation factor.


Vladimir Vassilevsky
DSP and Mixed Signal Designs
www.abvolt.com

On Wed, 19 Jun 2013 10:53:44 -0500, Vladimir Vassilevsky wrote:

> There is a need to estimate power which falls into given wide (~30% of
> Nyquist) bandwidth. Power spectrum doesn't matter; just overall number.
> The power estimate is not needed often; so a decimation factor of ~1000
> is preferred.
> 
> Straightforward way would be make FIR filter to cut out the bandwidth,
> run this filter at every 1000th sample, then measure power. But if the
> input is periodic or near periodic to decimated sample rate, then the
> power output would oscillate with difference frequency. This corresponds
> to comb response in spectral domain; ideally there should be flat
> response.
> 
> Is there an efficient way to deal with this problem? I am thinking of
> dithering decimation factor.

Your description is not clear.

Is the signal that you wish to measure the power of the only signal 
present?

Do you mean to decimate by 1000 and run your FIR filter on that, or do 
you mean that every 1000th sample you're going to run the entire FIR 
filter on as many samples as it has taps?

And when you say "but if the input is periodic..." do you mean that the 
input is affecting the power, and thus the _power_ may be periodic?

If the power is not steady and you dither the rate at which you sample 
it, then the best that you'll do is randomize the unsteadyness.  Then 
you'll be dealing with trying to estimate the power of a random signal.  
That's always a pain and a half, and often gets you highly varying and 
thus confusing results.

I dislike trying to measure power on anything but a nice steady signal -- 
when the signal isn't steady one quickly finds that "power" means 
different things to different people, that these "different things" often 
devolve down to the interval over which they are willing to average 
(which often depends on the thermal time constants of the things that 
they don't want to see burnt up, but may depend on the batteries and/or 
power supplies that they're using).  It can be difficult to satisfy all 
of one's customers in these cases.

My inclination would be to just measure the @#$% power continuously, 
unless I'm really backed into the wall for processing power.

-- 
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com

On Wed, 19 Jun 2013 10:53:44 -0500, Vladimir Vassilevsky
<nospam@nowhere.com> wrote:

>But if the input is periodic or near periodic to decimated sample rate, 
>then the power output would oscillate with difference frequency. This 
>corresponds to comb response in spectral domain; ideally there should be 
>flat response.

This is a sampling problem like any other. By analogy, if you
sample a sine wave that is very near half the sampling frequency,
you will get this same kind of "beat" behavior. The solution is to
observe a sufficiently long time series to cover a full period of
the "beat", so that the true signal can be reconstructed.

You can subsample to reduce the number of samples in the
observation, but the amount of TIME over which you must observe
the signal will not change.

Greg

>> dithering decimation factor

Sounds like a good idea to me. I'd sell it as a spread-spectrum method but
the result is the same. 

	 

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