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 signalimport matplotlib.pyplot as pltimport numpy as np |
Step 2: Defining the specifications of the IIR Bandpass Notch-Filter
Python3
# Create/view notch filtersamp_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.iirnotchb_notch, a_notch = signal.iirnotch(notch_freq, quality_factor, samp_freq)# Compute magnitude response of the designed filterfreq, 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 filterplt.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 frequenciesf1 = 15 # Frequency of 1st signal in Hzf2 = 50 # Frequency of 2nd signal in Hz# Set time vector# Generate 1000 sample sequence in 1 secn = np.linspace(0, 1, 1000) |
Step 6:
Python3
# Generate the signal containing f1 and f2noisySignal = 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
# Plottingfig = 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.filtfiltoutputSignal = signal.filtfilt(b_notch, a_notch, noisySignal) |
Step 9:
Python3
# Plot notch-filtered version of signalplt.subplot(212)# Plot output signal of notch filterplt.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 signalimport matplotlib.pyplot as pltimport numpy as np# Create/view notch filtersamp_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.iirnotchb_notch, a_notch = signal.iirnotch(notch_freq, quality_factor, samp_freq)# Compute magnitude response of the designed filterfreq, h = signal.freqz(b_notch, a_notch, fs=samp_freq)fig = plt.figure(figsize=(8, 6))# Plot magnitude response of the filterplt.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 frequenciesf1 = 15 # Frequency of 1st signal in Hzf2 = 50 # Frequency of 2nd signal in Hz# Set time vectorn = np.linspace(0, 1, 1000) # Generate 1000 sample sequence in 1 sec# Generate the signal containing f1 and f2noisySignal = np.sin(2*np.pi*15*n) + np.sin(2*np.pi*50*n) + \ np.random.normal(0, .1, 1000)*0.03# Plottingfig = 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.filtfiltoutputSignal = signal.filtfilt(b_notch, a_notch, noisySignal)# Plot notch-filtered version of signalplt.subplot(212)# Plot output signal of notch filterplt.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:
