1 | initial version |
An adaptive filter using the least mean squares (LMS) method can be implemented using Python by following these steps:
Step 1: Import the necessary libraries
import numpy as np
import matplotlib.pyplot as plt
Step 2: Define the input signal and the desired output signal
n = 500
x = np.random.normal(0, 1, n)
d = np.sin(2*np.pi*0.05*np.arange(n)) + np.random.normal(0, 0.1, n)
Step 3: Define the initial filter coefficients and the step size
w = np.zeros(10)
mu = 0.1
Step 4: Implement the LMS algorithm using a loop
y = np.zeros(n)
e = np.zeros(n)
for i in range(10, n):
y[i] = np.dot(w, x[i-10:i])
e[i] = d[i] - y[i]
w = w + mu * e[i] * x[i-10:i]
Step 5: Plot the input signal, the desired output signal, and the filtered output signal
plt.figure()
plt.subplot(311)
plt.plot(x)
plt.title('Input Signal')
plt.subplot(312)
plt.plot(d)
plt.title('Desired Output Signal')
plt.subplot(313)
plt.plot(y)
plt.title('Filtered Output Signal')
plt.show()
The full code is shown below:
import numpy as np
import matplotlib.pyplot as plt
n = 500
x = np.random.normal(0, 1, n)
d = np.sin(2*np.pi*0.05*np.arange(n)) + np.random.normal(0, 0.1, n)
w = np.zeros(10)
mu = 0.1
y = np.zeros(n)
e = np.zeros(n)
for i in range(10, n):
y[i] = np.dot(w, x[i-10:i])
e[i] = d[i] - y[i]
w = w + mu * e[i] * x[i-10:i]
plt.figure()
plt.subplot(311)
plt.plot(x)
plt.title('Input Signal')
plt.subplot(312)
plt.plot(d)
plt.title('Desired Output Signal')
plt.subplot(313)
plt.plot(y)
plt.title('Filtered Output Signal')
plt.show()