I want to calculate the derivative dY/dt but for that I need to smooth my input data (Y(t)) to get a coherent derivative.
I use the Gaussian kernel smoother because from what I have read for what I am trying to do, it is the most suitable.
The problem is that each time I have resulting vectors Y(t) of different sizes, the size can range from 100 to 3 million. In the same vector the time step is different because Delta T can be very low or very high (10-3 to 10) (low at the beginning then increases as you go along)
from what I understand, there are no rules for fixing window size or bandwidth in gaussian kernel smoother. I'd like to know if you have any indications on how to choose them.
I develop on C++, I don't know if it's useful to specify!