[time-nuts] measuring frequency

[jimlux]

David McClain wrote:
>> Or, now that I think about it, it's similar to what we do when 
>> measuring ADEV.. you can do a crude "how many zero crossings in the 
>> time window" or you can do a "fit a sinusoid to a series of ADC 
>> samples".  One has an uncertainty of "one count/epoch", the other can 
>> be substantially better.
> 
> 
> How could it be substantially better for the same analysis period? 
> Unless the frequency under test is an integral number of periods during 
> the analysis period, you will have a variation in the sine fitting due 
> to starting phase.

Say you have N>3 samples, evenly spaced spanning some reasonable number 
of cycles of the unknown+noise.
You fit f(i) = A*cos(B*i+C) {where i is the sample #} to the samples 
using any of a variety of techniques (least squares).

You can see that B isn't restricted to particular values that are 
multiples of 2*pi/N.

> 
> OTOH, as admonished in Horowitz & Hill, if the frequency to be counted 
> is substantially below your counter timebase, then you should count zero 
> crossings of the higher timebase frequency in the period of the lower 
> frequency under test.
> 

that's the "reciprocal counter" approach.