[time-nuts] exponential+linear fit

Magnus Danielson magnus at rubidium.dyndns.org
Sat Oct 5 11:18:36 EDT 2013


On 10/05/2013 04:48 PM, Jim Lux wrote:
> On 10/5/13 3:57 AM, Magnus Danielson wrote:
>> On 10/05/2013 01:03 AM, Jim Lux wrote:
>>> On 10/4/13 2:54 PM, Alan Melia wrote:
>>>> Jim it may not be helpful but had you thoughtof expanding the
>>>> exponential as the first few terms of an infinite series to see if it
>>>> simplifies fitting?
>
>>>
>>> I'll try attaching a plot of some sample data.
>> Oh, I/Q data, in that case recording the state of your tracking loop
>> helps a lot. Also, the rate of your exponential should be fairly well
>> known, so you could do a linear least square with that.
>>
>
> It's IQ but not from a tracking loop..
>
> The underlying physics is a turn on transient as it comes to
> temperature (with gain/phase variation) superimposed on a longer term
> linear trend.
Ah, OK.
> And it occurs to me that fitting more polynomial terms (although one
> can represent exp(x)+kx with a polynomial) runs the risk of removing
> the data (the variations in the I/Q), while constraining the fit to an
> exp(-kt) means that the "transient" starts at the beginning.
You will reduce your degrees of freedom with the amount of polynomial
terms you estimate and remove from the data. Your Pade approximation to
a+kx+b*exp(c*x) of say three terms of exp will consume 5 degrees of
freedom, but if you have thousands of samples you can live with it for
many uses. What kind of measure do you want to extract here really?
Noise-power?

Cheers,
Magnus


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