[time-nuts] Phase, One edge or two? (was Digital mixing with a D Flip Flop)
Tom Van Baak
tvb at LeapSecond.com
Wed Oct 22 16:59:51 EDT 2014
> Here is an extreme example of throwing away useful data for the sake of
> simplicity:
> When measuring phase drift of a 10 MHz osc using just a 1PPS signal,
> 19,999,999 other possible data points are being discarded.
> Using all possible data points could decrease the noise floor considerably.
> (by ~5,000 to 1)
Nice posting. A couple of comments that might help:
1) Depending on the resolution or quantization of your measurement system, more samples don't necessarily give you more information. Higher sample rates may help when the samples are statistically independent. When there is redundancy, you can fool yourself with more data. More data does not automatically imply more precision.
Imagine a very fast 1 GHz based counter which measures not 1PPS but all 10 million edges of a 10 MHz signal. It's quite likely, over a second, that all 10 million readings will be the same. So there is no 10,000,000 to 1 or even sqrt(10,000,000) = 3100 to 1 advantage here.
More averaging != more precision, except in very rare cases. The sqrt(N) trick you're thinking of works only if you have clean white noise (Gaussian distribution) and a static process. In general oscillators are more complex than this.
2) For long-term analysis, even 1 PPS is overkill. Having more data may not improve your oscillator drift plot at all. This is because the frequency is a moving target. Ever more precise measurements of a moving target are wasted; they don't add any clarity to the overall trend. Consider measuring a 10811 for a year. Do you need to follow its phase or frequency every 100 ns? Or second? Or minute? Maybe as little as one data point per day is more than enough to make a perfectly accurate long-term frequency drift plot.
3) Every instant on a sine wave is actually a data point, not just the zero crossing(s). So in reality there is near infinite information available. So is sample rate the limitation? Or is it sample resolution? Or something else too. How would having trillions of data points differ from 10 million data points from 100 data points from just 1, per second? What more would you know about the oscillator with more data? Are you after frequency domain measurements, or just time domain plots.
/tvb
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