How to Design FIR Filter: Simple Steps and Example

To design a FIR filter, first decide the filter type and specifications like cutoff frequency and order. Then use a window method or optimization technique to calculate filter coefficients, which define the filter's behavior.

Syntax

The basic syntax for designing a FIR filter using the window method in Python with scipy.signal is:

• firwin(numtaps, cutoff, window='hamming', pass_zero=True, fs=sample_rate)

Where:

• numtaps: Number of filter coefficients (filter order + 1)
• cutoff: Cutoff frequency or frequencies in Hz
• window: Type of window to shape the filter (e.g., 'hamming')
• pass_zero: True for lowpass, False for highpass
• fs: Sampling frequency of the signal

python

from scipy.signal import firwin

# Design a lowpass FIR filter
numtaps = 51  # filter length
cutoff = 1000  # cutoff frequency in Hz
fs = 8000  # sampling frequency in Hz

coefficients = firwin(numtaps, cutoff, window='hamming', pass_zero=True, fs=fs)

Example

This example shows how to design a lowpass FIR filter with a cutoff frequency of 1000 Hz, sampling rate 8000 Hz, and 51 taps. It also plots the frequency response to visualize the filter.

python

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

# Filter parameters
numtaps = 51
cutoff = 1000
fs = 8000

# Design filter
coefficients = firwin(numtaps, cutoff, window='hamming', pass_zero=True, fs=fs)

# Frequency response
w, h = freqz(coefficients, worN=8000, fs=fs)

# Plot
plt.plot(w, 20 * np.log10(abs(h)), 'b')
plt.title('Frequency Response of FIR Filter')
plt.xlabel('Frequency (Hz)')
plt.ylabel('Gain (dB)')
plt.grid(True)
plt.show()

Output

A plot window showing the frequency response curve with a clear cutoff near 1000 Hz and attenuation above cutoff.

Common Pitfalls

• Choosing too few taps results in poor filter sharpness and more ripple.
• Not matching the cutoff frequency to the sampling rate causes wrong filtering.
• Using the wrong window type can increase side lobes and ripple.
• For highpass filters, pass_zero must be set to False.

python

from scipy.signal import firwin

# Wrong: cutoff frequency higher than Nyquist frequency
numtaps = 51
cutoff = 5000  # Wrong if fs=8000, Nyquist=4000
fs = 8000

# This will cause incorrect filter design
coefficients_wrong = firwin(numtaps, cutoff, window='hamming', pass_zero=True, fs=fs)

# Right: cutoff less than Nyquist frequency
cutoff_correct = 3000
coefficients_right = firwin(numtaps, cutoff_correct, window='hamming', pass_zero=True, fs=fs)

Quick Reference

Tips for FIR filter design:

• Number of taps controls filter sharpness and delay.
• Cutoff frequency must be less than half the sampling rate (Nyquist).
• Window choice affects ripple and transition width.
• Use freqz to check frequency response visually.

Key Takeaways

Design FIR filters by choosing filter order, cutoff frequency, and window type carefully.

Ensure cutoff frequency is below Nyquist frequency (half the sampling rate).

Use window methods like Hamming to control ripple and transition sharpness.

Visualize filter response with frequency plots to verify design.

Set pass_zero parameter correctly for lowpass or highpass filters.