Design an IIR Notch Filter to Denoise Signal using Python

IIR stands for Infinite Impulse Response, It is one of the striking features of many linear-time invariant systems that are distinguished by having an impulse response h(t)/h(n) which does not become zero after some point but instead continues infinitely.

What is IIR Notch Filter?

A Notch Filter is a bandstop filter with a very narrow stopband and two passbands, it actually highly attenuates/eliminates a particular frequency component from the input signal while leaving the amplitude of the other frequencies more or less unchanged.

The specifications are as follows:  

• Generate a signal of 15 Hz corrupted with 50 Hz power line frequency.
• Sampling frequency: 1 kHz

Approach:

Step 1: Importing all the necessary libraries.

Python3

from scipy import signal
import matplotlib.pyplot as plt
import numpy as np

Step 2: Defining the specifications of the IIR Bandpass Notch-Filter

Python3

# Create/view notch filter
samp_freq = 1000  # Sample frequency (Hz)
notch_freq = 50.0  # Frequency to be removed from signal (Hz)
quality_factor = 20.0  # Quality factor

Step 3:

Python3

# Design a notch filter using signal.iirnotch
b_notch, a_notch = signal.iirnotch(notch_freq, quality_factor, samp_freq)

# Compute magnitude response of the designed filter
freq, h = signal.freqz(b_notch, a_notch, fs=2*np.pi)

Step 4:

Python3

fig = plt.figure(figsize=(8, 6))

# Plot magnitude response of the filter
plt.plot(freq*samp_freq/(2*np.pi), 20 * np.log10(abs(h)),
         'r', label='Bandpass filter', linewidth='2')

plt.xlabel('Frequency [Hz]', fontsize=20)
plt.ylabel('Magnitude [dB]', fontsize=20)
plt.title('Notch Filter', fontsize=20)
plt.grid()

Output:

Step 5:

Python3

# Create and view signal that is a mixture
# of two different frequencies
f1 = 15  # Frequency of 1st signal in Hz
f2 = 50  # Frequency of 2nd signal in Hz

# Set time vector
# Generate 1000 sample sequence in 1 sec
n = np.linspace(0, 1, 1000)

Step 6:

Python3

# Generate the signal containing f1 and f2
noisySignal = np.sin(2*np.pi*15*n) + np.sin(2*np.pi*50*n) + \
    np.random.normal(0, .1, 1000)*0.03

Step 7:

Python3

# Plotting
fig = plt.figure(figsize=(8, 6))
plt.subplot(211)
plt.plot(n, noisySignal, color='r', linewidth=2)
plt.xlabel('Time', fontsize=20)
plt.ylabel('Magnitude', fontsize=18)
plt.title('Noisy Signal', fontsize=20)

Output:

Step 8:

Python3

# Apply notch filter to the noisy signal using signal.filtfilt
outputSignal = signal.filtfilt(b_notch, a_notch, noisySignal)

Step 9:

Python3

# Plot notch-filtered version of signal
plt.subplot(212)

# Plot output signal of notch filter
plt.plot(n, outputSignal)
plt.xlabel('Time', fontsize=20)
plt.ylabel('Magnitude', fontsize=18)
plt.title('Filtered Signal', fontsize=20)
plt.subplots_adjust(hspace=0.5)
fig.tight_layout()
plt.show()

Output:

Below is the implementation:

Python3

from scipy import signal
import matplotlib.pyplot as plt
import numpy as np

# Create/view notch filter
samp_freq = 1000  # Sample frequency (Hz)
notch_freq = 50.0  # Frequency to be removed from signal (Hz)
quality_factor = 20.0  # Quality factor

# Design a notch filter using signal.iirnotch
b_notch, a_notch = signal.iirnotch(notch_freq, quality_factor, samp_freq)

# Compute magnitude response of the designed filter
freq, h = signal.freqz(b_notch, a_notch, fs=samp_freq)

fig = plt.figure(figsize=(8, 6))

# Plot magnitude response of the filter
plt.plot(freq*samp_freq/(2*np.pi), 20 * np.log10(abs(h)),
         'r', label='Bandpass filter', linewidth='2')
plt.xlabel('Frequency [Hz]', fontsize=20)
plt.ylabel('Magnitude [dB]', fontsize=20)
plt.title('Notch Filter', fontsize=20)
plt.grid()

# Create and view signal that is a mixture of two different frequencies
f1 = 15  # Frequency of 1st signal in Hz
f2 = 50  # Frequency of 2nd signal in Hz
# Set time vector
n = np.linspace(0, 1, 1000)  # Generate 1000 sample sequence in 1 sec

# Generate the signal containing f1 and f2
noisySignal = np.sin(2*np.pi*15*n) + np.sin(2*np.pi*50*n) + \
    np.random.normal(0, .1, 1000)*0.03

# Plotting
fig = plt.figure(figsize=(8, 6))
plt.subplot(211)
plt.plot(n, noisySignal, color='r', linewidth=2)
plt.xlabel('Time', fontsize=20)
plt.ylabel('Magnitude', fontsize=18)
plt.title('Noisy Signal', fontsize=20)

# Apply notch filter to the noisy signal using signal.filtfilt
outputSignal = signal.filtfilt(b_notch, a_notch, noisySignal)

# Plot notch-filtered version of signal
plt.subplot(212)

# Plot output signal of notch filter
plt.plot(n, outputSignal)
plt.xlabel('Time', fontsize=20)
plt.ylabel('Magnitude', fontsize=18)
plt.title('Filtered Signal', fontsize=20)
plt.subplots_adjust(hspace=0.5)
fig.tight_layout()
plt.show()

Output: