Table of Contents

In [1]:

    

import numpy as np
import matplotlib.pyplot as plt


    

In [4]:

    

a = np.linspace(-np.pi, np.pi, 200)
b = np.cos(a)
c = b + np.random.randn(200) * 0.3


    

In [19]:

    

plt.figure(figsize=(12, 9))
plt.plot(a, b, linewidth=4, color="yellow")
plt.scatter(a, c, color='red')
plt.legend(["Cosine", "Samples"], fontsize=16)
plt.show()


    

In [16]:

    

d = [c[0]]
for i in range(1, c.shape[0]):
    d.append(0.8 * d[i - 1] + 0.2 * c[i])


    

In [39]:

    

plt.figure(figsize=(12, 9))
plt.plot(a, b, linewidth=4, color="yellow")
plt.scatter(a, c, color="red")
plt.plot(a, d, linewidth=3, color="blue")
plt.legend(["Cosine", "Moving Average", "Samples"], fontsize=16)
plt.show()


    

In [32]:

    

d1 = [c[0]]
for i in range(1, c.shape[0]):
    d1.append(0.9 * d1[i - 1] + 0.1 * c[i])
d2 = [c[0]]
for i in range(1, c.shape[0]):
    d2.append(0.97 * d2[i - 1] + 0.03 * c[i])
d3 = [c[0]]
for i in range(1, c.shape[0]):
    d3.append(0.5 * d3[i - 1] + 0.5 * c[i])


    

In [38]:

    

plt.figure(figsize=(12, 9))
plt.plot(a, b, linewidth=4, color="yellow")
plt.scatter(a, c, color="red")
plt.plot(a, d3, linewidth=3, color="cyan")
plt.plot(a, d1, linewidth=3, color="blue")
plt.plot(a, d2, linewidth=3, color="gray")
plt.legend(["Cosine", r"$\beta=0.5$", r"$\beta=0.9$", r"$\beta=0.97$", "Samples"], fontsize=16)
plt.show()


    

In [ ]: