我试图以每 160us（微秒）采样一次 12.8 MHz 正弦波（78.125 ns）信号。由于 160us 是基周期 78.125ns(x2048) 的倍数，我希望得到一个固定幅度的样本，但我看到的是另一个周期性正弦波。我不明白为什么？
我怀疑量化误差，但不应该产生均匀的噪声而不是产生周期性的正弦波。
import numpy as np
from matplotlib import pyplot as plt
fig2 = plt.figure()
ax2 = fig2.add_subplot(1, 1, 1)
capture_size1 = 2048
timestep1 = 160e-6
freq1 = 12.8e6
time1 = np.linspace(0, capture_size1 * timestep1, capture_size1)
w1 = np.sin(time1 * 2 * np.pi * freq1)
ax2.plot(time1, w1, '.')
plt.show()
Edit1 : 1. 12.8 MHZ 故意采样不足
- 在 capture_size1 = 2048 的情况下添加绘图的屏幕截图，正弦波的适当幅度为 [+1, -1]
Edit2：我尝试通过使用 Decimal 来提高精度，我发现它的行为符合预期。我期望一条直线，因为采样点是周期的精确倍数。
from decimal import Decimal
from math import pi as mpi
from math import sin as msin
import numpy as np
from matplotlib import pyplot as plt
fig2 = plt.figure()
ax2 = fig2.add_subplot(1, 1, 1)
capture_size1 = 2048
timestep1 = 160e-6
freq1 = 12.8e6
time1 = np.linspace(0, capture_size1 * timestep1, capture_size1)
w1 = np.sin(time1 * 2 * np.pi * freq1)
ax2.plot(time1, w1, '.')
capture_size3 = Decimal(2048 * 16)
timestep3 = Decimal(160e-6)
freq3 = Decimal(12.8e6)
time3 = [Decimal(i) * timestep3 for i in range(capture_size1)]
w3 = [msin(Decimal(i) * timestep3 * Decimal(2) * Decimal(mpi) * freq3) for i in range(capture_size1)]
ax2.plot(time3, w3, '.')
plt.legend(["Actual", "Expected"])
plt.show()
Edit3：感谢@jithin 的评论，我进一步做了一些分析。看起来这是 linspace 的问题。我尝试通过乘法来生成时间间隔，如下面的代码所示，并删除了使用 linspace 的原始图（这是至关重要的），所以现在我可以看到其他人建议的 1e-9 范围内的值。那么 linspace 确实存在问题吗？
from decimal import Decimal
from math import pi as mpi
from math import sin as msin
import numpy as np
from matplotlib import pyplot as plt
fig2 = plt.figure()
ax2 = fig2.add_subplot(1, 1, 1)
capture_size1 = 2048
# timestep1 = 160e-6
# freq1 = 12.8e6
# time1 = np.linspace(0, capture_size1 * timestep1, capture_size1)
# w1 = np.sin(time1 * 2 * np.pi * freq1)
# ax2.plot(time1, w1, '.')
capture_size2 = 2048
timestep2 = 160e-6
freq2 = 12.8e6
time2 = [i * timestep2 for i in range(capture_size2)]
w2 = [np.sin(i * timestep2 * 2 * np.pi * freq2) for i in range(capture_size2)]
ax2.plot(time2, w2, '.')
capture_size3 = Decimal(2048)
timestep3 = Decimal(160e-6)
freq3 = Decimal(12.8e6)
time3 = [Decimal(i) * timestep3 for i in range(capture_size1)]
w3 = [msin(Decimal(i) * timestep3 * Decimal(2) * Decimal(mpi) * freq3) for i in range(capture_size1)]
ax2.plot(time3, w3, '.')
plt.legend(["multiply", "Decimal"], fontsize='xx-large')
plt.show()
上述python代码的图像如下
