Finding exponential decay of a*e^(-t*b)*sin(c*t) function

For a project I need to find the exponential decay of a a*e^(-t*b)*sin(c*t) function.

After which i can determine the q factor with the resonance frequency(determined with fft). When the signal is clear i managed this by using the envelope function. I did this by first plotting this exponential function and then determining where the e^-1 point was. The signal looked like this:

Now i want to try it with noise and ofcourse the envelope function will not work. Using a lowpass filter does not work very wel due to(i think) the changing amplitude. Is there an other way to determine this exponential part of this function? With noise it looks something like this:

Some suggestions would be very helpfull, thankyou.

Answer 1

[Star Strider]

See if fitting it will do what you want. See for example How to filter noise from time-frequency data and find natural frequency of a cantilever? That will calculate several parameters, including the decay constant.