Convenience functions for pulses

[RemDelaporteMathurin]

It would be convenient to have functions like periodic step function, periodic step function with ramp up/down etc.

def periodic_step_function(x, period_on, period_total, value_on, value_off=0.0):
    """
    Creates a periodic step function with two periods.
    """

    if period_total < period_on:
        raise ValueError("period_total must be greater than period_on")
    
    if x % period_total < period_on:
        return value_on
    else:
        return value_off

[RemDelaporteMathurin]

We also need a trapezoidal membership function:

[RemDelaporteMathurin]

Maybe something like this would work:

def periodic_trapezoidal_membership_function(x, period, a, b, c, d, value_on=1.0, value_off=0.0):
    """
    Creates a periodic trapezoidal membership function.
    
    Parameters:
    x : float
        The input value.
    period : float
        The period of the function.
    a : float
        The start of the rising edge within one period.
    b : float
        The start of the top edge within one period.
    c : float
        The end of the top edge within one period.
    d : float
        The end of the falling edge within one period.
    value_on : float
        The value during the plateau (top edge).
    value_off : float
        The value outside the trapezoid (when x < a or x > d).
    
    Returns:
    float
        The membership value.
    """
    x_mod = x % period
    if x_mod < a or x_mod > d:
        return value_off
    elif a <= x_mod < b:
        return value_off + (value_on - value_off) * (x_mod - a) / (b - a)
    elif b <= x_mod <= c:
        return value_on
    elif c < x_mod <= d:
        return value_off + (value_on - value_off) * (d - x_mod) / (d - c)