import numpy as np
import matplotlib.pyplot as plt


def main():
    n = np.arange(7)        # n ranges from 0 to 7 (not including 7)
    x = np.array([1, -5, 4, -8, 6, -3, -1])

    x_1 = x[(n+3) % 7]      # x[ <n+3>_7 ]
    x_2 = x[(n-4) % 7]      # x[ <n-4>_7 ]
    x_3 = x[(-n+2) % 7]     # x[ <-n+2>_7 ]

    plt.subplot(411)
    plt.stem(n,x)
    plt.ylabel("$x[n]$")

    plt.subplot(412)
    plt.stem(n,x_1)
    plt.ylabel(r"$x[\langle n+3 \rangle_7]$")

    plt.subplot(413)
    plt.stem(n, x_2)
    plt.ylabel(r"$x[\langle n-4\rangle_7]$")

    plt.subplot(414)
    plt.stem(n, x_3)
    plt.ylabel(r"$x[\langle -n+2\rangle_7]$")

    plt.xlabel("$n$")
    plt.show()



if __name__ == "__main__":
    main()