#Let for example:
x, t = step(H,t)

#Then we could use these to analyse the response:
def overshoot(x,t):
    """
    Indicates the overshoot point of the response.
    :param x: Vector containing the response to an input.
    :param t: Vector containing the corresponding time.
    :return: The maximum value of the overshoot (M),
    the time at which the maximum overshoot value occurs (T),
    and the percentage overshoot (p).
    """
    x = np.array(x).reshape(-1)
    t = np.array(t).reshape(-1)
    f = x[-1]
    M = np.max(x)
    T = t[np.argmax(x)]
    p = (M/f - 1) * 100
    return M, T, p

def settling(x,t,th=0.05):
    """
    Indicates the time for the system to settle
    to withing the specified threshold.
    :param x: Vector containing the response to an input.
    :param t: Vector containing the corresponding time.
    :param th: Threshold for the settling time.
    :return: The value of the response at the settling point (S) and
    the settling time (T).
    """
    x = x.reshape(-1)
    t = t.reshape(-1)
    filter = np.logical_or(x > x[-1]*(1+th), x < x[-1]*(1-th))
    T = t[filter][-1]
    idx = np.where(t==T)
    S = float(x[idx])
    return S, T

def delay(x,t,th=0.1):
    """
    Indicates the time for the system to reach an initial
    specified threshold.
    :param x: Vector containing the response to an input.
    :param t: Vector containing the corresponding time.
    :param th: Threshold for the delay time.
    :return: The value of the response at the delay point (D) and
    the delay time (T).
    """
    x = x.reshape(-1)
    t = t.reshape(-1)
    filter = np.where(x >= th*x[-1])
    T = t[filter][0]
    idx = np.where(t == T)
    D = float(x[idx])
    return D, T

def rise(x,t,th_rise=0.9,no_delay=True,th_delay=0.1):
    """
    Indicates the time for the system to reach a specified percentage
    of the final response.
    :param x: Vector containing the response to an input.
    :param t: Vector containing the corresponding time.
    :param th_rise: Threshold for the rise time.
    :param th_delay: Threshold for the delay time.
    :param no_delay: If True, it will not consider the delay time in the rise time.
    :return: The value of the response at the rise point (R) and
    the rise time (T).
    """
    x = x.reshape(-1)
    t = t.reshape(-1)
    filter = np.where(x >= th_rise * x[-1])
    R = x[filter][0]
    if no_delay == True:
        T = t[filter][0] - delay(x,t,th_delay)[1]
    else:
        T = t[filter][0]
    return R, T

def characteristics(x,t,th_del=0.1,th_ris=0.9,th_set=0.05,no_delay=True):
    """
    Computes the 4 main characteristics of a response: delay time, rise time,
    overshoot, and settling time.
    :param x: Vector containing the response to an input.
    :param t: Vector containing the corresponding time.
    :param th_del: Threshold for the delay time.
    :param th_ris: Threshold for the rise time.
    :param th_set: Threshold for the settling time.
    :param no_delay: If True, it will not consider the delay time in the rise time.
    :return: Tuples containing time and value for said characteristics.
    """
    ovs = overshoot(x, t)
    set = settling(x, t,th_set)
    dey = delay(x,t,th_del)
    ris = rise(x,t,th_ris,no_delay,th_del)
    return ovs,set,dey,ris