Poul said;
"If you tell me it is a sine and give me the time of two zero crossings
I can tell you everything there has or ever will be to know ..."
just to add a bit more nut picking on comment #3.
When talking about sub picosecond per second time nut type accuracy, there
is no such thing as a pure "analog" sinewave.
so the answer becomes circular in that it takes more than two samples to
tell exactly where the two zero crossing points are.
Even if there was a near perfect sinewave with under -120 db of bad stuff,
and the perfect sine to square wave converter with an exactally known time
delay and no zero offset error, and a brick wall low pass cutoff,
Given just two data points, it is going to be a real challenge to calculate
everything such as Freq, Phase, amplitude, Johnson noise and bandwidth.
Add in the typical harmonics, sub harmonics, freq spurs, cycle to cycle
changes, cross talk, line noise, ADC resolution, etc, along with a less
than perfect signal to noise ratio, and the number of samples needed to get
a good enough answer is increased even further.
Nyquist says it takes greater than two samples per cycle to be able to even
tell if there is any higher freq content present.
These are some of the reasons I believe when starting with a signal in the
analog world, it helps to oversample, until you can get the data into the
pure digital world where one time-stamped sample per cycle can then give you
the signal's freq and phase.
ws
********************
"Poul-Henning Kamp" Posted
Just to pick a nit here: That depends precisely on what and how
you measure.
If you measure phase, then no, you probably don't need to measure
more often than one phase difference per hour or even day, as long
as you can reliably predict (from the frequency including noise)
exactly how many periods were in that hour or day.
This is basically what timelabs do: They measure against some radio
signal (GPS, Two-Way, etc. etc.) every so often, trusting their
stability between measurements.
If you measure frequency, you MUST measure the frequency continously
at all times without any deadtime between the measurements to get
the precise result. The advantage is that you make *no* assumptions
about the frequency or its stability at all.
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.
Sorry, but no.
If you tell me it is a sine and give me the time of two zero crossings
I can tell you everything there has or ever will be to know about any
point on that sine-wave.
Where looking at the whole curve makes sense is if it is not a
sinewave, either because it is a complex signal (Loran's 3rd crossing)
or because the sinewave is distorted in a way (ie: non-harmonic)
which can be averaged out by looking at the entire curveform
(locking onto a received radio signal.)
But for pure sine signals or good approximations, measuring the
zero crossing tells you all you can ever learn.
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