MATLAB Source Code for Designing Butterworth Low-Pass Filters

This MATLAB source code provides a complete implementation for designing a Butterworth low-pass filter, a fundamental tool in signal processing applications. The program utilizes MATLAB's built-in filter design functions (such as butter) to generate filter coefficients based on specified parameters including cutoff frequency, filter order, and sampling rate. The implementation follows the standard Butterworth filter design methodology, which maximizes flatness in the passband region while providing smooth roll-off characteristics. Key algorithmic steps involve: calculating normalized frequency specifications, determining pole locations using analog prototype transformation, and converting to digital filter coefficients through bilinear transformation. Users can modify critical parameters like the cutoff frequency (typically normalized as Wn) and filter order (N) to achieve specific amplitude response requirements. The code serves as both a practical filtering solution and an educational resource for understanding Butterworth filter properties, including its maximally flat magnitude response in the passband. Before execution, ensure MATLAB is installed with the Signal Processing Toolbox, and basic familiarity with MATLAB syntax and filter design concepts is recommended for optimal utilization.