How to Implement FIR Filter in Python: Simple Guide

To implement a FIR filter in Python, you can use the scipy.signal.lfilter function with filter coefficients created by scipy.signal.firwin. This applies the filter to your data by convolving it with the FIR coefficients.

Syntax

The basic syntax to apply a FIR filter in Python is:

• firwin(numtaps, cutoff, window='hamming', pass_zero='lowpass'): Creates FIR filter coefficients.
• lfilter(b, a, x): Applies the filter to data x using coefficients b and denominator a.

For FIR filters, a is usually 1 because FIR filters have only zeros (no poles).

python

from scipy.signal import firwin, lfilter

# Create FIR filter coefficients
numtaps = 51  # Number of filter taps (coefficients)
cutoff = 0.3  # Normalized cutoff frequency (0 to 1, where 1 is Nyquist frequency)
coefficients = firwin(numtaps, cutoff, window='hamming')

# Apply FIR filter to data
# b = coefficients, a = 1 for FIR filter
filtered_signal = lfilter(coefficients, 1, [1, 2, 3, 4, 5])

Example

This example shows how to create a low-pass FIR filter and apply it to a noisy sine wave signal to smooth it.

python

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import firwin, lfilter

# Generate sample data: noisy sine wave
fs = 500  # Sampling frequency in Hz
T = 1.0   # seconds
t = np.linspace(0, T, int(fs*T), endpoint=False)
signal = np.sin(2 * np.pi * 5 * t) + 0.5 * np.random.randn(len(t))

# Design FIR filter
numtaps = 101
cutoff = 0.1  # Normalized cutoff frequency (0 to 1, where 1 is Nyquist frequency)
coefficients = firwin(numtaps, cutoff, window='hamming')

# Apply FIR filter
filtered_signal = lfilter(coefficients, 1, signal)

# Plot original and filtered signals
plt.figure(figsize=(10, 6))
plt.plot(t, signal, label='Noisy Signal')
plt.plot(t, filtered_signal, label='Filtered Signal', linewidth=2)
plt.xlabel('Time [seconds]')
plt.ylabel('Amplitude')
plt.title('FIR Filter Applied to Noisy Signal')
plt.legend()
plt.grid(True)
plt.show()

Output

A plot showing the noisy sine wave and the smoother filtered signal over time.

Common Pitfalls

• Wrong cutoff frequency: The cutoff must be normalized between 0 and 1, where 1 is the Nyquist frequency (half the sampling rate).
• Filter delay: FIR filters introduce delay equal to half the filter length; this can shift your signal in time.
• Using lfilter vs filtfilt: lfilter applies filter once causing phase delay; filtfilt applies forward and backward to remove delay but doubles computation.
• Filter length too short: Too few taps can cause poor filtering; too many taps increase computation.

python

from scipy.signal import filtfilt

# Using lfilter (causes delay)
filtered_lfilter = lfilter(coefficients, 1, signal)

# Using filtfilt (zero phase delay)
filtered_filtfilt = filtfilt(coefficients, 1, signal)

Quick Reference

Here is a quick summary of key FIR filter steps in Python:

Step	Function	Description
Design filter	firwin(numtaps, cutoff)	Create FIR coefficients
Apply filter	lfilter(b, 1, x)	Filter signal x with coefficients b
Remove delay	filtfilt(b, 1, x)	Zero-phase filtering (optional)

Step	Function	Description
Design filter	firwin(numtaps, cutoff)	Create FIR coefficients
Apply filter	lfilter(b, 1, x)	Filter signal x with coefficients b
Remove delay	filtfilt(b, 1, x)	Zero-phase filtering (optional)

Key Takeaways

Use scipy.signal.firwin to create FIR filter coefficients with desired cutoff.

Apply the FIR filter to data using scipy.signal.lfilter with denominator 1.

Normalize cutoff frequency between 0 and 1, where 1 is Nyquist frequency.

FIR filters introduce delay; use filtfilt to remove phase delay if needed.

Choose filter length (numtaps) carefully for balance between smoothness and performance.