[time-nuts] exponential+linear fit

[Jim Lux]

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.

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.