如何在Python中测试线性(叠加)和移不变性？

import numpy as np
import matplotlib.pyplot as plt

def test_linearity():
    # 创建输入信号
    x1 = np.linspace(0, 10, 100)
    x2 = np.linspace(0, 5, 100)

    # 创建输出信号
    y1 = 2 * x1 + 3 * x2
    y2 = 2 * x1 + x2

    # 绘制输入信号和输出信号的图形
    plt.plot(x1, label='Input Signal x1')
    plt.plot(x2, label='Input Signal x2')
    plt.plot(y1, label='Output Signal y1')
    plt.plot(y2, label='Output Signal y2')
    plt.legend()
    plt.show()

def test_invariance():
    # 创建输入信号
    x = np.linspace(0, 10, 100)

    # 创建输出信号
    y1 = 2 * x
    y2 = 2 * (x - 1)

    # 绘制输入信号和输出信号的图形
    plt.plot(x, label='Input Signal x')
    plt.plot(y1, label='Output Signal y1')
    plt.plot(y2, label='Output Signal y2')
    plt.legend()
    plt.show()

# 调用测试函数
test_linearity()
test_invariance()