o_transform transforms "time series signal of values" to "current values taking past values into account in each terms"

o_transform.py

import numpy as np

def o_transform(signal):
    ret = []
    for n in range(1, len(signal)+1):
        a = 2 / (n + 1)
        d = -2 / (n * (n + 1))

        s = 0
        for t in range(n):
            s += signal[t] * (a + t * d)
        ret.append(s)
    
    return np.array(ret)

o_transform's definition is

where

or you can choose any monotonically decreasing function which suffices