[time-nuts] measuring frequency

David McClain dbm at refined-audiometrics.com
Thu Oct 14 13:28:49 UTC 2010


No, it isn't restricted to an integral number of periods, but you  
will have a higher variance in your fits unless there are, due to  
variations of the fit with respect to initial phase.

I don't want to send this thread in the wrong direction... but we  
have to agree on apples vs apples comparisons. How many samples per  
second are being counted, versus what is the sample rate in the ADC?

Offhand, I totally agree with you, but that is a gut instinct. And  
what I'm trying to do is force a showdown between gut instinct and  
facts. Are there facts that would back this assertion?

Dr. David McClain
Chief Technical Officer
Refined Audiometrics Laboratory
4391 N. Camino Ferreo
Tucson, AZ  85750

email: dbm at refined-audiometrics.com
phone: 1.520.390.3995
web: http://refined-audiometrics.com



On Oct 14, 2010, at 06:16, jimlux wrote:

> 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.
>
>
>
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