I have a damped, tuned circuit and want to measure its Q factor. The hardware sends an impulse 'ping' and samples the output as it rings down.
Is there an efficient way to fit an equation of the form $A e^{t(i\omega + b)} $ to a series of samples? I know $\omega$ up front, and $A$ isn't relevant. I am primarily interested in the value of $b$.
For my system the Q factors I want to measure are in the range 2-5, and the amplitude of the noise is about 10% of the signal.
My current solution uses a Goertzel filter to measure the energy at the frequency of interest for each of the successive cycles, then looks for the point where the magnitude drops by a quarter. With some interpolation between the cycles before and after the quarter point, this gives reasonable but not great results. It is especially bad for the low end of the Q range.