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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