Re: [Discuss-gnuradio] Using DSP for precise zero crossing, measurement?

[John Ackermann N8UR]

Lee Patton wrote:
> Thanks, Bob -
>
> I think this problem is a little trickier than previously assumed
> because:
>
> 1) I believe John wants to measure frequency drift over time (i.e.,
> drift of one clock with respect to a reference)  So, the clock signals
> cannot be assumed to be 100% coherent.  Otherwise, there would be no
> drift to measure.  The problem here is that there is no underlying model
> for how this drift occurs. (It's what he's trying to find out!)  The
> signals are probably very close to coherent over some finite window, but
> the problem becomes one of determining a window size that helps
> integrate out noise but doesn't do too much averaging of the drifting
> signal to obtain parameter estimates.

The two signals are definitely not coherent.  The offset is likely to be 
small, but it's there.

The real goal is not to measure the long term drift, but rather the 
short term variation (i.e., if the deltat between F1 and F2 is 1us, how 
much does it wiggle around that 1us value from second to second).

> 2) John wants to measure to the best possible accuracy.  So, while we
> assume A1=A2=1, this might not be the best assumption.  Even if he
> measures the amplitude at the output of his clocks, there is no
> guarantee that both digitizing channels are completely calibrated.  They
> may be "good enough," but that depends on his application.

Ideally, I'd like to avoid measuring the amplitude with any device other 
than the ADC that's being used for the sampling.

> 3) Relating to (1), I think John needs estimates of instantaneous
> frequency over time.  A sliding window method similar to the one
> outlined below would work. Again though, how is the window size chosen
> if the nature of the drift isn't known?  Similarly, there are adaptive
> techniques that could be used.  They should track to some degree, but
> again, at what point do they break lock, and how do we know?

You got it.

As you all know, I'm no mathematician.  On the airplane ride home from 
the Digital Communications Conference Sunday night, my friend Tom (who's 
an RF engineer but not a DSP theory guy) and I roughed out a simple idea 
like this (please feel free to laugh and throw things):

1.  determine when the slope of the waveform was positive.

2.  start grabbing samples at some point shortly before the nominal zero 
crossing.

3.  continue grabbing samples until some point shortly after the nominal 
zero crossing.

4.  use an appropriate set (e.g., the endpoints, or a least-squares fit) 
of those samples to determine the slope of the signal around the zero 
crossing.

5.  find the two samples that most closely bracket the zero crossing, 
and use the slope derived in step 4 to interpolate between those two 
samples to find the real zero crossing time.

6.  use any extra samples in some magical way to
decrease the impact of any noise on the interpolation (told you, we 
aren't statisticians or DSP experts!).

7.  timestamp the samples so we can determine the time between zero 
crossing of F1 and zero crossing of F2

8.  log that difference to later feed to the Allan Deviation program

One interesting question was whether we were better served in this 
algorithm by having more bits in the ADC for better voltage 
discrimination, or a higher sample rate for better frequency discrimination.

I'm sure that this method has serious flaws, but perhaps the zero 
crossing has the advantage of being amplitude-independent (so long as 
you stay close enough to the middle of the waveform so that the slope is 
approximately constant).

John