MATLAB Programming Implementation of Butterworth Low-Pass and Band-Pass Filters

In this article, we will implement Butterworth low-pass and band-pass filters using MATLAB programming. These filters are essential tools in digital signal processing, commonly used for removing unwanted high-frequency noise or selecting specific frequency ranges of interest. Through MATLAB programming, we can flexibly design and adjust filter parameters to meet specific application requirements. The Butterworth low-pass filter serves to smooth signals and reduce noise in signal processing, while the band-pass filter selectively transmits signals within a particular frequency range. Therefore, mastering the programming implementation of these filters is crucial for both learning and applying digital signal processing techniques.

Key implementation aspects include using MATLAB's Signal Processing Toolbox functions such as butter() for filter coefficient calculation, filter() for signal processing, and freqz() for frequency response analysis. The butter() function requires specifying filter order and cutoff frequencies, where low-pass filters need a single cutoff frequency while band-pass filters require two cutoff frequencies defining the passband. The filter design process typically involves determining specifications, calculating coefficients, applying the filter, and analyzing results through frequency and time-domain plots.