I'm trying to transform a time series with a recursive filter to model a feedback.
I was able to do a simple filter like :
Y[t] = x +αY[t-1] a*y[n] = b*x[n] + b*x[n-1]
but i don't know how i can model this kind of transformation with a filter:
Y = α (1 - e^(1 - β x)) + Y[T-1]
the desired effect is:
x = time_series data feedback = .35 alfa = .40 beta = 10 transformed = np.empty(len(x.values)) for k in range(0, len(transformed )): if k == 0: transformed[k] = x else: transformed[k] = (alfa* (1-np.exp(-beta*x[k])) ) + feedback*transformed[k-1]