def __init__(self, order: int) -> None:
        self.order = order

        # a_{0} ... a_{k}
        self.a_coeffs = [1.0] + [0.0] * order
        # b_{0} ... b_{k}
        self.b_coeffs = [1.0] + [0.0] * order

        # x[n-1] ... x[n-k]
        self.input_history = [0.0] * self.order
        # y[n-1] ... y[n-k]
        self.output_history = [0.0] * self.order