Notch Filter: Definition, How It Works, and Examples

A notch filter is a signal processing tool that removes or reduces a very narrow range of frequencies from a signal while leaving others mostly unchanged. It is often used to eliminate unwanted noise or interference at a specific frequency, like the 60 Hz hum from electrical power lines.

How It Works

A notch filter works like a very selective gate that blocks out a tiny band of frequencies while letting all other frequencies pass through. Imagine you are listening to music but there is a single annoying beep at one pitch. The notch filter acts like a sound-proof wall that only blocks that beep's pitch, so the rest of the music sounds normal.

Technically, it creates a deep dip or "notch" in the frequency response at the unwanted frequency. This notch is very narrow, so frequencies just above or below it are mostly unaffected. This precision makes notch filters ideal for removing specific interference without harming the overall signal.

Example

This example shows how to create a notch filter in Python using the SciPy library to remove a 60 Hz noise from a signal.

python

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

fs = 1000  # Sampling frequency in Hz
f0 = 60    # Frequency to remove (notch frequency)
Q = 30     # Quality factor (controls notch width)

# Create a sample signal: 5 Hz sine wave + 60 Hz noise
T = 1.0
t = np.linspace(0, T, int(fs*T), endpoint=False)
signal = np.sin(2*np.pi*5*t) + 0.5*np.sin(2*np.pi*60*t)

# Design notch filter
b, a = iirnotch(f0, Q, fs)

# Apply notch filter
filtered_signal = filtfilt(b, a, signal)

# Plot results
plt.figure(figsize=(10, 6))
plt.plot(t, signal, label='Original Signal')
plt.plot(t, filtered_signal, label='Filtered Signal', linestyle='--')
plt.xlabel('Time [seconds]')
plt.ylabel('Amplitude')
plt.title('Notch Filter Removing 60 Hz Noise')
plt.legend()
plt.grid(True)
plt.show()

Output

A plot showing the original signal with a 60 Hz noise and the filtered signal where the 60 Hz noise is removed, leaving the 5 Hz sine wave clear.

When to Use

Use a notch filter when you need to remove a very specific frequency from a signal without affecting other parts. Common cases include:

• Removing electrical hum at 50 or 60 Hz from audio or sensor data.
• Eliminating narrowband interference in communication signals.
• Cleaning biomedical signals like ECG or EEG from power line noise.

Because notch filters target a narrow frequency range, they are perfect when the noise frequency is known and stable.

Key Points

• A notch filter removes a narrow band of frequencies from a signal.
• It is highly selective, affecting only the unwanted frequency.
• Commonly used to remove power line interference (50/60 Hz).
• Implemented using digital or analog filter designs.
• Quality factor (Q) controls the width of the notch.

Key Takeaways

A notch filter removes a very narrow frequency band from a signal.

It is ideal for eliminating specific interference like 60 Hz electrical noise.

The filter’s quality factor controls how sharply it targets the unwanted frequency.

Notch filters preserve most of the original signal outside the notch.

They are widely used in audio, communications, and biomedical signal cleaning.