Band-pass and band-stop filters in Signal Processing

Introduction

Band-pass and band-stop filters help us keep or remove specific ranges of signals. This is useful to focus on important parts or remove noise.

To listen only to a certain range of radio frequencies and ignore others.

To remove unwanted noise from a sound recording that is outside the main signal range.

To isolate a specific frequency range in an ECG signal for heart analysis.

To block interference signals in communication systems.

To analyze only a certain band of frequencies in vibration data from machines.

Syntax

Signal Processing

band_pass_filter(signal, low_cutoff, high_cutoff)
band_stop_filter(signal, low_cutoff, high_cutoff)

band_pass_filter keeps frequencies between low_cutoff and high_cutoff.

band_stop_filter removes frequencies between low_cutoff and high_cutoff, keeping others.

Examples

This keeps frequencies between 100 Hz and 300 Hz in the signal.

Signal Processing

filtered_signal = band_pass_filter(signal, 100, 300)

This removes frequencies between 50 Hz and 60 Hz, often used to remove power line noise.

Signal Processing

clean_signal = band_stop_filter(signal, 50, 60)

Sample Program

This program creates a signal with two frequencies: 50 Hz and 200 Hz. It then applies a band-pass filter to keep only the 40-60 Hz range and a band-stop filter to remove that same range. The first 5 samples of each result are printed to show the effect.

Signal Processing

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import butter, filtfilt

# Create a sample signal with mixed frequencies
fs = 1000  # Sampling frequency in Hz
T = 1.0    # seconds
n = int(T * fs)
t = np.linspace(0, T, n, endpoint=False)

# Signal with 50 Hz and 200 Hz components
signal = np.sin(2 * np.pi * 50 * t) + 0.5 * np.sin(2 * np.pi * 200 * t)

# Define band-pass filter function

def band_pass_filter(data, lowcut, highcut, fs, order=4):
    nyq = 0.5 * fs
    low = lowcut / nyq
    high = highcut / nyq
    b, a = butter(order, [low, high], btype='band')
    y = filtfilt(b, a, data)
    return y

# Define band-stop filter function
def band_stop_filter(data, lowcut, highcut, fs, order=4):
    nyq = 0.5 * fs
    low = lowcut / nyq
    high = highcut / nyq
    b, a = butter(order, [low, high], btype='bandstop')
    y = filtfilt(b, a, data)
    return y

# Apply band-pass filter to keep 40-60 Hz
bp_filtered = band_pass_filter(signal, 40, 60, fs)

# Apply band-stop filter to remove 40-60 Hz
bs_filtered = band_stop_filter(signal, 40, 60, fs)

# Print first 5 values of each signal
print('Original signal samples:', signal[:5])
print('Band-pass filtered samples:', bp_filtered[:5])
print('Band-stop filtered samples:', bs_filtered[:5])

Important Notes

Band-pass filters keep only the frequencies inside the chosen range.

Band-stop filters remove frequencies inside the chosen range and keep others.

Choosing the right cutoff frequencies depends on your signal and what you want to keep or remove.

Summary

Band-pass filters keep signals only in a specific frequency range.

Band-stop filters remove signals in a specific frequency range.

These filters help clean or focus on parts of signals in real-world data.