1- Phenomenological classification :

1- Deterministic signals :

2- Random signals :

2- Energy classification :

1- Finite energy signals :

2- Signals at finite average power :

3- Morphological classification :

Special signals :

Sign function :

import numpy as np 
def sign(x):
    return np.sign(x)

Step function :

import numpy as np
def step(t,t0=0):
    return np.where(t>=t0,1,0)

Rect function :

def p(t):
    return 1 * (abs(t) < 0.5)