import numpy as np
import matplotlib.pyplot as plt

def main():
    # Define the samples axis (0 to 51, excluding 51)
    n = np.arange(51)
    
    # Define the four frequencies used
    f_1 = 1/7
    f_2 = 1/21
    f_3 = 1/17.5
    f_4 = 1/(7*np.pi)

    # Convert frequencies to angular frequency
    omega_1 = 2*np.pi*f_1
    omega_2 = 2*np.pi*f_2
    omega_3 = 2*np.pi*f_3
    omega_4 = 2*np.pi*f_4

    # Sample a cosine of each of the 
    x_1 = np.cos(omega_1*n)
    x_2 = np.cos(omega_2*n)
    x_3 = np.cos(omega_3*n)
    x_4 = np.cos(omega_4*n)
    
    # Plot each of the cosines in a separate subplot
    plt.subplot(411)
    plt.stem(n, x_1)

    plt.subplot(412)
    plt.stem(n, x_2)

    plt.subplot(413)
    plt.stem(n, x_3)

    plt.subplot(414)
    plt.stem(n, x_4)
    plt.xlabel("n")

    plt.show()


if __name__ == "__main__":
    main()