[time-nuts] Re: Fixing PN degradation via ADEV measurement

[Magnus Danielson]

Hi Jim,

On 2022-06-20 17:57, Lux, Jim via time-nuts wrote:
> On 6/20/22 2:39 AM, Magnus Danielson via time-nuts wrote:
>>
>>
>> So, a counter is really like an ADC for phase, with wide bandwidth 
>> input and a sub-sampling mechanism (trigger/time-base). Through 
>> processing frequency estimates can be provided. Aliasing occurrs in 
>> the sub-sampling. Modern counters can provided estimation filters 
>> than goes from a higher sub-sampling rate to a lower, which to some 
>> degree removes aliasing, but not fully. These frequency estimation 
>> methods form a form of decimation filter.
>>
>> Cheers,
>> Magnus 
>
> An intruiging thought as I drink my first cup of coffee (meaning it's 
> not well thought out)..
Enjoy!
>
> jumping off from "counter is similar to an ADC for phase" - is there a 
> time domain equivalent for Nyquist criterion?   Certainly there's the 
> cycle ambiguity.. you know when the zerocrossing occurred, but not how 
> many are in between (although a counter usually does). For everything 
> else there is a frequency/time duality, so I suspect there is.  The 
> criterion is usually explained in terms of information - so there 
> should be an equivalent "has all the information" statement for 
> counters/gate widths/precisions.

Well, considering that optimum phase/time sensitivity is at the 
through-zero of a sine, with the optimum slew-rate of the signal, you 
have two observation points per cycle. You can view that as having 
essentially two sample-points of phase per cycle. Similarly you will 
have two optimal sample-points for amplitude in quadrature on the peaks 
of the sine.

Now, using this fact, you have a Nyquistian type of relationship and 
also upper phase-information frequency being that of the cosine itself, 
since you can fit a modulaiton that pushes the rising edge one way and 
the falling edge the other way. As you attempt a higher modulation 
frequency you cannot distinguish that from the mirror frequency lower 
than that frequency. Thus, they Nyquist frequency of modulation is the 
carrier frequency.

But then again, the same can be said for any overtones, so you can 
support higher modulation frequencies there, with the same basic rule. 
However, sorting that out can be a bit tricky, considering non-linear 
functions and intermodulations.

PS. IEEE Std. 1139-2022 made it through a formal approval after 
balloting, so now it is off for last editorial touch-ups before 
publishing. Good news. Look forward to put it into use.

Cheers,
Magnus

>
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