两个时间序列的水平位移，对两者互信息值的影响

两个时间序列（时序信号）的水平位移（重叠程度），对两者互信息值的影响

1、x和y完全重叠；

MIStimulation(xspike=100, yspike=100)

2、x和y相差1

MIStimulation(xspike=100, yspike=101)

3、x和y相差10

MIStimulation(xspike=100, yspike=110)

3、x和y相差100

MIStimulation(xspike=100, yspike=200)

结论：信号在时序上的重叠程度会影响MI。为什么会出现这种结果呢，因为计算MI时，会计算两者的联合概率分布，当两个信号不重叠的时候，联合概率分布基本上处处为0，所以MI也基本上为0；

def MIStimulation(xspike=500, yspike=500):
    x = np.zeros(1000)
    y = np.zeros(1000)
    ratio = 0.94
    x[xspike] = 2
    for i in range(xspike+1,xspike+200):
        x[i] = x[i-1] * ratio
        # print(x[i])
    y[yspike] = 2
    for i in range(yspike+1,yspike+200):
        y[i] = y[i-1] * ratio
        # print(y[i])

    mi = calMI(x, y)

    fig, ax = plt.subplots()
    ax.plot(x)
    ax.plot(y)
    ax.set_title('xspike is {}, yspike is {}. MI between x and y is {:.2f}'.format(xspike, yspike, mi))
    fig.show()

    print()