In this article, the task is to write a Python program for Noise Removal using Lowpass Digital Butterworth Filter.
What is the noise?
Noise is basically the unwanted part of an electronic signal. It is often generated due to fault in design, loose connections, fault in switches etc.
What to do if we have noise in our signal?
To remove unwanted signals/noise we use filters of different types and specifications. Generally in the industry we need to choose the best fit by testing it with the signal to pinpoint the best filter to be used for removing the noise in a given use case.
What are we going to do now?
We are going to implement a Lowpass Digital Butterworth Filter now to remove the unwanted signal/noise of a combination of sinusoidal waves.
Filter Specifications:
- Signal made up of 25 Hz and 50 Hz
- Sampling frequency 1kHz.
- Order N=10 at 35Hz to remove 50Hz tone.
Step by Approach:
Step 1:Importing the libraries
# import required library import numpy as np
import scipy.signal as signal
import matplotlib.pyplot as plt
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Step 2:Defining the specifications
# Specifications of the filter f1 = 25 # Frequency of 1st signal
f2 = 50 # Frequency of 2nd signal
N = 10 # Order of the filter
# Generate the time vector of 1 sec duration t = np.linspace( 0 , 1 , 1000 ) # Generate 1000 samples in 1 sec
# Generate the signal containing f1 and f2 sig = np.sin( 2 * np.pi * f1 * t) + np.sin( 2 * np.pi * f2 * t)
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Step 3:Plot the original signal with noise
# Display the signal fig, (ax1, ax2) = plt.subplots( 2 , 1 , sharex = True )
ax1.plot(t, sig) ax1.set_title( '25 Hz and 50 Hz sinusoids' )
ax1.axis([ 0 , 1 , - 2 , 2 ])
# Design the Butterworth filter using # signal.butter and output='sos' sos = signal.butter( 50 , 35 , 'lp' , fs = 1000 , output = 'sos' )
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Output:
Step 4:Plot of the signal after removing noise
# Filter the signal by the filter using signal.sosfilt # Use signal.sosfiltfilt to get output inphase with input filtered = signal.sosfiltfilt(sos, sig)
# Display the output signal ax2.plot(t, filtered) ax2.set_title( 'After 35 Hz Low-pass filter' )
ax2.axis([ 0 , 1 , - 2 , 2 ])
ax2.set_xlabel( 'Time [seconds]' )
plt.tight_layout() plt.show() |
Output:
Step 5: Implementation
# import required library import numpy as np
import scipy.signal as signal
import matplotlib.pyplot as plt
# Given f1 = 25 # Frequency of 1st signal
f2 = 50 # Frequency of 2nd signal
N = 10 # Order of the filter
# Generate the time vector of 1 sec duration # START CODE HERE ### (≈ 1 line of code) # Generate 1000 samples in 1 sec t = np.linspace( 0 , 1 , 1000 )
# Generate the signal containing f1 and f2 # START CODE HERE ### (≈ 1 line of code) sig = np.sin( 2 * np.pi * f1 * t) + np.sin( 2 * np.pi * f2 * t)
# Display the signal fig, (ax1, ax2) = plt.subplots( 2 , 1 , sharex = True )
ax1.plot(t, sig) ax1.set_title( '25 Hz and 50 Hz sinusoids' )
ax1.axis([ 0 , 1 , - 2 , 2 ])
# Design the Butterworth filter using signal.butter and output='sos' # START CODE HERE ### (≈ 1 line of code) sos = signal.butter( 50 , 35 , 'lp' , fs = 1000 , output = 'sos' )
# Filter the signal by the filter using signal.sosfilt # START CODE HERE ### (≈ 1 line of code) # Use signal.sosfiltfilt to get output inphase with input filtered = signal.sosfiltfilt(sos, sig)
# Display the output signal ax2.plot(t, filtered) ax2.set_title( 'After 35 Hz Low-pass filter' )
ax2.axis([ 0 , 1 , - 2 , 2 ])
ax2.set_xlabel( 'Time [seconds]' )
plt.tight_layout() plt.show() |
Output: