"""
ECE 09351 - Digital Signal Processing
Lab 1 Question 2

Translated from MATLAB by Aidan Sharpe
Last Modified: January 16, 2025
"""


import numpy as np
import matplotlib.pyplot as plt



def main():
    f_sweep = np.arange(1,25)*np.pi                             # Angular frequency sweep from pi to 24*pi
    f_max = np.max(f_sweep)                                     # Maximum frequency in the frequency sweep
    f_s = 2*f_max                                               # Sample frequency at twice maximum
    T_s = 1/f_s                                                 # Sampling period

    E = np.empty_like(f_sweep)                                  # Array to store energy calculations
    for i, f in enumerate(f_sweep):                             # Loop over all frequencies in sweep
        W = np.arange(0, f, T_s)                                # Define the variable of integration
        x = np.sinc(0.5*W/np.pi)                                # np.sinc(0.5*W/np.pi) = sinc(0.5*W)
        E[i] = np.sum(x**2 * T_s)/np.pi                         # Integrate x^2, with dt = T_s

    plt.stem(f_sweep, E)                                        # Plot energy at each frequency in sweep
    plt.hlines(0.99, f_sweep[0], f_sweep[-1], colors="red")     # Red horizontal line at 99% total energy
    plt.xlabel("Angular frequency")
    plt.ylabel("Signal energy")
    plt.show()



if __name__ == "__main__":
    main()