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August 26, 2025 12:07
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| import numpy as np | |
| import matplotlib.pyplot as plt | |
| import sys | |
| Ts = 0.000001 | |
| n_cycles = 240000 | |
| if len(sys.argv) > 1: | |
| n_cycles = int(sys.argv[1]) | |
| t = np.arange(0, n_cycles * Ts, Ts) | |
| A2 = 0.06 | |
| f1, theta1, fd1, f2, theta2, fd2 = 300, 0, 0, 400, np.pi / 3, 4 | |
| s1 = np.cos(2 * np.pi * (f1 + fd1) * t + theta1) | |
| s2 = A2 * np.cos(2 * np.pi * (f2 + fd2) * t + theta2) | |
| sign_plot = np.int8(np.sign(s1 + s2)) | |
| successive_difference = sign_plot[1:] - sign_plot[:-1] | |
| # plt.stem(t, sign_plot, label=r'$\text{sign}(s_1(t) + s_2(t)) - \text{sign}(s_1(t))$') | |
| # plt.legend() | |
| # plt.figure() | |
| # plt.stem(successive_difference) | |
| # plt.show() | |
| up_jumps = np.where(successive_difference == 2)[0] + 1 | |
| down_jumps = np.where(successive_difference == -2)[0] + 1 | |
| def phi(t, A, f1, f2, fd2, theta2): | |
| return np.atan2(A * np.sin(2 * np.pi * (f2 - f1 + fd2) * t + theta2), | |
| 1 + A * np.cos(2 * np.pi * (f2 - f1 + fd2) * t + theta2)) | |
| # In up jumps, the phase should be 3pi / 2 | |
| idx = up_jumps[7] | |
| t_up_jump = t[idx] | |
| phi_idx = phi(t_up_jump, A2, f1, f2, fd2, theta2) | |
| total_phase = phi_idx + 2 * np.pi * f1 * t_up_jump | |
| total_phase = np.mod(total_phase, 2 * np.pi) | |
| if total_phase > np.pi: total_phase -= 2 * np.pi | |
| print(total_phase) | |
| # In down jumps, the phase should be pi / 2 | |
| idx = down_jumps[6] | |
| t_down_jump = t[idx] | |
| phi_idx = phi(t_down_jump, A2, f1, f2, fd2, theta2) | |
| total_phase = phi_idx + 2 * np.pi * f1 * t_down_jump | |
| total_phase = np.mod(total_phase, 2 * np.pi) | |
| if total_phase > np.pi: total_phase -= 2 * np.pi | |
| print(total_phase) | |
| def wrap_angle(total_phase): | |
| total_phase = np.mod(total_phase, 2 * np.pi) | |
| if total_phase > np.pi: total_phase -= 2 * np.pi | |
| return total_phase | |
| # Let's get rid of 2 * pi * f1 * t | |
| phi_only_list = [] | |
| for t_up_jump in t[up_jumps]: | |
| print(f"LOOP_DEBUG: {wrap_angle(2 * np.pi * f1 * t_up_jump + phi(t_up_jump, A2, f1, f2, fd2, theta2))}") | |
| phi_only = wrap_angle(np.pi * 3 / 2 - 2 * np.pi * f1 * t_up_jump) | |
| print(f"LOOP_DEBUG: {phi(t_up_jump, A2, f1, f2, fd2, theta2)}, {phi_only}") | |
| phi_only_list.append(phi_only) | |
| for t_down_jump in t[down_jumps]: | |
| phi_only = np.pi / 2 - 2 * np.pi * f1 * t_down_jump | |
| phi_only_list.append(wrap_angle(phi_only)) | |
| tan_vals = np.tan(phi_only_list) | |
| print(np.max(np.abs(tan_vals))) |
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