Designing Digital Filters Using Butterworth Filter in MATLAB

This article explores how to design digital filters using Butterworth filters in MATLAB. Digital filters represent a fundamental concept in digital signal processing (DSP), serving critical functions such as noise removal and frequency characteristic enhancement in signals. As widely applied tools in DSP, mastering digital filter design and implementation is essential for signal processing engineers.

First, we need to understand the Butterworth filter characteristics. The Butterworth filter is a linear-phase filter type used for digital filter design, featuring smooth frequency response and rapid roll-off characteristics. Compared to other digital filters, its key advantage lies in achieving desired performance with lower filter order, thereby reducing computational complexity and memory requirements. This makes it a popular choice for practical digital filter implementations.

This tutorial demonstrates Butterworth filter design in MATLAB with practical implementation guidance. We will cover fundamental filter concepts and utilize MATLAB's Filter Design Toolbox functions such as butter() for coefficient calculation and filtfilt() for zero-phase filtering. The article explains critical parameter selection including filter order determination using buttord() and cutoff frequency specification. Finally, we'll implement the filter using MATLAB code structures like: [b,a] = butter(n,Wn) for transfer function coefficients y = filtfilt(b,a,x) for signal processing Visualization techniques using fvtool() will demonstrate frequency response characteristics. Through this comprehensive guide, you'll gain practical skills to design and deploy Butterworth filters in real-world applications.