matrix/signals.py at master · Xtinc/matrix · GitHub

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import array
import numpy as np
from scipy import signal
import matplotlib.pyplot as plt
import tools.misc as misc

plt.style.use("tools.gnuplot")
plt.axis("equal")


def Hu(u):
    nu = u / np.linalg.norm(u)
    return np.eye(2) - 2 * nu @ np.transpose(nu)


u = np.array([[3, 1]]).T
line1 = np.array([[0, 0], [0.25, 1], [0.5, 2], [0.75, 3], [1, 4]])
line2 = np.array([Hu(u) @ np.array(ele) for ele in line1])
plt.plot(line2[:, 0], line2[:, 1], "x-")
plt.plot(line1[:, 0], line1[:, 1], "x-")
plt.plot([0, 3], [0, 1], label=r"$u$")
plt.plot([-1, 1], [3, -3], label=r"$u_\bot$")
plt.legend()

# N = 2048 * 5  # 采样点的个数
# x = np.arange(0, 2 * np.pi, 2 * np.pi / N)
# fs = N / (2 * np.pi)
# # 产生频率为120、500、10hz的信号进行模拟
# y = (
#     7 * np.sin(120 * 2 * np.pi * x)
#     + 5 * np.sin(500 * 2 * np.pi * x)
#     + 9 * np.sin(10 * 2 * np.pi * x)
#     + np.random.normal(scale=np.sqrt(1.89), size=len(x))
# )
# fre, amp, _ = misc.fft(y, fs)
# plt.plot(fre, amp)
# w = np.arange(0, N, 1)  # 频域轴


# b1 = signal.firwin(
#     51, [0.42, 0.8], window="hamming", pass_zero="bandstop"
# )  # 哈明窗，截至频率100Hz
# b2 = [
#     0.0010176,
#     0.000927711,
#     -0.00238796,
#     0.000434621,
#     -0.00010929,
#     0.00253823,
#     0.00180104,
#     -0.00843451,
#     0.00289083,
#     0.00124462,
#     0.00682364,
#     0.00227208,
#     -0.0243103,
#     0.0124667,
#     0.00617722,
#     0.0127504,
#     -0.00127084,
#     -0.0580584,
#     0.0431386,
#     0.0189968,
#     0.0179269,
#     -0.0191777,
#     -0.172457,
#     0.224718,
#     0.120414,
#     0.619334,
#     0.120414,
#     0.224718,
#     -0.172457,
#     -0.0191777,
#     0.0179269,
#     0.0189968,
#     0.0431386,
#     -0.0580584,
#     -0.00127084,
#     0.0127504,
#     0.00617722,
#     0.0124667,
#     -0.0243103,
#     0.00227208,
#     0.00682364,
#     0.00124462,
#     0.00289083,
#     -0.00843451,
#     0.00180104,
#     0.00253823,
#     -0.00010929,
#     0.000434621,
#     -0.00238796,
#     0.000927711,
#     0.0010176,
# ]
# w1, h = signal.freqz(b1)  # 求频响
# w2, h2 = signal.freqz(b2)

# plt.figure(1)
# plt.title("Frequence Response")
# plt.plot(w1 / 2 / np.pi * N, 20 * np.log10(np.abs(h) + 0.01))
# plt.xlabel("$f$")
# plt.ylabel("$H(f)$")
# plt.plot(w2 / 2 / np.pi * N, 20 * np.log10(np.abs(h2) + 0.01))

# b2 = signal.firwin(24, 2 * 100 / N, window="hann")  # 汉宁窗，截至频率100Hz
# w1, h = signal.freqz(b2)  # 求频响
# plt.figure(2)
# plt.title("freqz")
# plt.plot(w1 / 2 / np.pi * N, 20 * np.log10(np.abs(h) + 0.01))

# b3 = signal.firwin(24, 2 * 100 / N, window="blackman")  # 布莱克曼窗，截至频率100Hz
# w1, h = signal.freqz(b3)  # 求频响
# plt.figure(3)
# plt.title("freqz")
# plt.plot(w1 / 2 / np.pi * N, 20 * np.log10(np.abs(h) + 0.01))

# b4 = signal.firwin(N, 2 * 100 / N, window="boxcar")  # 矩形窗，截至频率100Hz
# w1, h = signal.freqz(b4)  # 求频响
# plt.figure(4)
# plt.title("freqz")
# plt.plot(w1 / 2 / np.pi * N, 20 * np.log10(np.abs(h) + 0.01))
plt.show()