"基于MATLAB的数字滤波器优化设计研究"

In the field of digital signal processing, digital filters are widely used for signal processing. There are two main types of digital filters: Finite Impulse Response (FIR) filters and Infinite Impulse Response (IIR) filters. This thesis focuses on the design and implementation of these two types of digital filters. For FIR filters, this study discusses two main issues: the characteristics and derivation of relevant formulas for FIR linear phase filters, and the design of FIR filters using window functions. Specifically, the study highlights the optimization design of FIR digital filters based on the equiripple Chebyshev approximation criteria, and demonstrates the implementation through MATLAB simulations. For IIR filters, the design process is broken down into three steps: designing the analog filter prototype, transforming the analog filter into a digital filter, and transforming the filter frequency band. The study emphasizes the direct design method and optimization design method in the frequency domain. The design process for both types of filters follows a structured approach of theoretical analysis, programming design, and practical implementation. Key words: Digital filters; MATLAB; Optimization design algorithms; Impulse response.