Butterworth Design Method for IIR Digital Filters

This documentation presents the Butterworth design approach for IIR digital filters. The implementation includes comprehensive time-domain and frequency-domain analysis of both input and output signals. The Butterworth filter design algorithm focuses on achieving maximally flat frequency response in the passband, making it ideal for applications requiring minimal ripple. Key MATLAB functions employed in this implementation include butter() for filter coefficient calculation and freqz() for frequency response analysis. The design process involves specifying filter order and cutoff frequencies, then applying bilinear transformation for digital filter realization. These analytical plots provide crucial insights into filter performance characteristics, including magnitude response, phase behavior, and transient response. While digital filter design can be complex, the Butterworth method offers a systematic approach to achieve desired filtering effects with predictable performance. Understanding this design methodology is essential for engineers and researchers working on signal processing applications. The code implementation demonstrates practical applications of filter design theory with visual validation through comparative signal analysis.