[time-nuts] exponential+linear fit

[Magnus Danielson]

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?
>
> Hmm..
>
> So the tradeoff is "fit polynomial with higher order" (because the
> polynomial basically is the first few terms of a Taylor expansion for
> exp(x)).  My DC and linear term in X basically add to the terms for
> the exponential.
> vs
> linearize the data by taking the log of each point, then fit a
> straight line.
>
> Without grinding through a benchmark, I have to believe that
> calculating the various powers of the inputs to do a least squares has
> to be computationally lighter load than doing log, and then exp
>
>
> 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.

Your tracking-loops dynamics is a significant hint to after the fact
compensate for the lock-in behavior.

Cheers,
Magnus