Digital Bandpass Filter Design using Chebyshev Method

Digital filters are computational devices or programs that process digital input signals to modify the relative proportions of frequency components or eliminate specific frequencies through numerical operations. Classical digital filters are categorized based on their filtering characteristics into low-pass, high-pass, band-pass, and band-stop types. The magnitude response of a digital filter indicates the amplitude attenuation of frequency components after passing through the filter, while the phase response reflects the time delays introduced to each frequency component.

This course project begins with an introduction to the theoretical foundations of Chebyshev digital bandpass filters. The Chebyshev filter is a common digital filter type with specific filtering characteristics suitable for bandpass applications. Based on performance indicator analysis, we will implement a design program using MATLAB's buttord function (for determining filter order and cutoff frequencies) and butter function (for generating filter coefficients). The implementation involves calculating transfer function coefficients and plotting the loss function (magnitude response in dB) and phase response curves. These visualizations help evaluate filter performance across different frequencies, including passband ripple and stopband attenuation characteristics. Finally, we will derive the digital filter system function H(z) in rational polynomial form, which serves as the core function for practical filter implementation using difference equations.

Through this course project, we will gain deep insights into digital filter principles and applications, along with Chebyshev filter design methodology. This foundation will support further learning and applications in digital signal processing领域, enabling efficient frequency-domain manipulation of signals using standardized MATLAB filter design routines.