According to this and many other places, weight for exponential moving average is just being defined as $\omega_t=(1-\alpha)\alpha^t$, where $t$ is current index and $\alpha$ is a smoothing factor.
How does one derives this formula itself and what does $\alpha$ mean, and where does one can plug size of averaging window?
This is the problem for me as I expected $\omega$ to be a function of window size $N$ and index $t$, but here and everywhere else I got only $t$ and mysterious $\alpha$.
I understand that $0<\alpha<1$ and that it describes the steepness of the exponential slope, but I am confused that I cant find the derivation of this formula. That is why I cant understand it to the end. Could anybody provide step by step derivation of this?