卷积是怎么【卷】的

# coding:utf-8
"""
Author:  CVPy-冰不语
Date:    2019/11/26
"""  
  
import numpy as np
import matplotlib.pyplot as plt


# 定义函数f(x)
def f(x):
    """$f\ (\\tau)$"""
    return x


# 定义函数g(x)
def g(x):
    """$f(x)=sin(x)$"""
    return np.sin(x/10)


# 设置坐标系
def set_ax(ax):
    ax.spines['top'].set_color('none')
    ax.spines['right'].set_color('none')
    ax.spines['bottom'].set_color('deepskyblue')
    ax.spines['left'].set_color('deepskyblue')

    ax.xaxis.set_ticks_position('bottom')
    ax.spines['bottom'].set_position(('data', 0))
    ax.yaxis.set_ticks_position('left')
    ax.spines['left'].set_position(('data', 0))

    ax.set_xticks(np.arange(-100,101, 50))
    # ax.set_yticks(np.arange(-100,101, 50))

    return ax


if __name__ == "__main__":
    # x的取值范围
    x = np.arange(-100, 100, 0.1)

    # ---------第一幅图：f(x)和f(-x)----------
    fig = plt.figure(figsize=(6, 6))

    # 左边画f(x)
    ax1 = fig.add_subplot(121)
    ax1 = set_ax(ax1)
    ax1.plot(x, f(x), 'orange', label=f.__doc__)
    plt.legend(loc="upper left", bbox_to_anchor=[0, 1],
               ncol=1, fancybox=True)

    # 右边画f(-x)
    ax2 = fig.add_subplot(122)
    ax2 = set_ax(ax2)
    plt.plot(x, f(-x), 'orange', label="$f\ (-\\tau)$")
    plt.legend(loc="upper right", bbox_to_anchor=[1, 1],
               ncol=1, fancybox=True)
    plt.show()

    # ---------第二幅图：f(t-x)----------
    fig2 = plt.figure(figsize=(6, 6))
    ax3 = fig2.add_subplot(111)

    ax3 = set_ax(ax3)
    ax3.set_xticks(np.arange(-100, 101, 20))
    ax3.set_yticks(np.arange(-100, 181, 20))

    for t in [20, 40, 60, 80]:
        plt.plot(x, f(t-x), label="$f\ (x_0 - \\tau) \ \ x_0={0}$".format(t))
    plt.legend(loc="upper right", bbox_to_anchor=[1, 1], ncol=1, fancybox=True)

    plt.show()

    # ---------第三幅图：g(x) * f(t-x)----------
    t = 80


    def f_mul_g(x, t):
        """$f(\\tau-x)*g(\\tau)$"""
        return f(t-x)*g(x)

    fig3, ax4 = plt.subplots()

    ax4 = set_ax(ax4)
    ax4.set_xticks(np.arange(-100,101, 20))
    # ax4.set_yticks(np.arange(-100,181, 20))

    plt.plot(x, f_mul_g(x, t), label=f_mul_g.__doc__)
    plt.legend(loc="upper right", bbox_to_anchor=[1, 1], ncol=1, fancybox=True)

    plt.show()

    # ---------第四幅图：g(x) * f(t-x)的积分----------
    import matplotlib.patches as mPatches


    def int_fg(x, t, ax5):
        ax5 = set_ax(ax5)

        plt.plot(x,f_mul_g(x, t), 'orange', label="$f\ (\\tau)*g(x_0-\\tau) \ \  x_0={0}$".format(t))
        plt.legend(loc="upper right", bbox_to_anchor=[1, 1],
                   ncol=1, fancybox=True)

        a = -50
        b = 50
        ix = np.linspace(a,b)
        iy = f_mul_g(ix,t)

        verts = [(a,0)] + list(zip(ix, iy)) + [(b,0)]
        poly = mPatches.Polygon(verts,color='deepskyblue')
        ax5.add_patch(poly)
        # plt.plot(x,g(x),label=g.__doc__)

        plt.text(30, 50, '$\int_a^b f\ (\\tau)*g(x_0-\\tau) \ \  x_0={0}$'.format(t), style='oblique',
                 bbox={'facecolor': 'orange', 'alpha': 0.5, 'pad': 5}, fontsize=15)

    fig4, ax5 = plt.subplots()
    int_fg(x, t, ax5)
    plt.legend(loc="upper right", bbox_to_anchor=[1, 1], ncol=1, fancybox=True)

    plt.ion()

    # for i in range(100):

    #     y = np.random.random()

    #     plt.autoscale()

    #     plt.scatter(i, y)

    #     plt.pause(0.01)

    fig4, ax5 = plt.subplots()
    tn = np.arange(-100,100,5)
    for t in tn:
        plt.cla()
        plt.grid(True)
        plt.autoscale()
        int_fg(x, t, ax5)
        plt.pause(0.01)

        plt.legend(loc="upper right", bbox_to_anchor=[1, 1], ncol=1, fancybox=True)

    plt.show()