FIR滤波器设计中窗函数的选择与性能权衡研究
Selection of Window Functions and Performance Trade-offs in FIR Filter Design
摘要
在数字信号处理领域，数字滤波器是实现信号筛选、频谱分析及干扰消除等功能的核心组件。其中，有限长冲激响应滤波器因其绝对稳定性与严格线性相位特性，在对波形保真度要求严苛的高保真音频、高速通信及生物医学信号处理等应用中至关重要。窗函数法作为FIR滤波器最经典直观的设计方法，其物理概念清晰、实现简便，是理解滤波器设计原理的重要基础。本文首先系统阐述了FIR滤波器实现线性相位的数学条件及其充要条件，深入剖析了窗函数法的设计原理及其频谱卷积机制。在此基础上，重点研究了矩形窗、汉宁窗、汉明窗和布莱克曼窗四种典型窗函数的频域特性，详细探讨了主瓣宽度与旁瓣峰值衰减等关键参数对滤波器性能的决定性影响。通过MATLAB仿真平台，设计并实现了一个具有特定指标的低通FIR滤波器实例，定量对比分析了不同窗函数在通带波纹、阻带最小衰减及过渡带宽度等关键性能指标上的表现。实验结果以详尽图表数据清晰揭示了窗函数选择中存在的"过渡带锐度"与"阻带抑制能力"之间的固有权衡关系。本研究不仅为初学者理解FIR滤波器设计提供了完整的理论框架，其结论更为工程实践中窗函数的科学选型与滤波器参数的优化设计提供了坚实的理论依据与可行的实践指导。
Abstract
In the field of digital signal processing, digital filters serve as core components for functions such as signal screening, spectral analysis, and interference elimination. Among them, Finite Impulse Response (FIR) filters are crucial in applications demanding high waveform fidelity, such as high-fidelity audio processing, high-speed communication, and biomedical signal analysis, due to their inherent absolute stability and strict linear phase characteristics. The window function method, as one of the most classic and intuitive design approaches for FIR filters, features clear physical concepts and straightforward implementation, providing an essential foundation for understanding filter design principles. This paper first systematically elaborates on the mathematical conditions and necessary/sufficient criteria for FIR filters to achieve linear phase. It then delves into the design principles of the window function method and its underlying spectral convolution mechanism. Furthermore, the frequency-domain characteristics of four typical window functions-Rectangular, Hanning, Hamming, and Blackman windows-are studied in detail, with a focus on how key parameters like mainlobe width and sidelobe peak attenuation decisively influence final filter performance. Using the MATLAB simulation platform, a low-pass FIR filter with specified specifications was designed and implemented as a case study. The performance of different window functions was quantitatively compared across key metrics including passband ripple, minimum stopband attenuation, and transition bandwidth. Experimental results, presented through comprehensive graphs and data, clearly reveal the inherent trade-off between "transition band sharpness" and "stopband rejection capability" during window function selection. This research not only provides a complete theoretical framework for beginners to understand FIR filter design but also offers solid theoretical foundations and practical guidance for engineers in scientifically selecting window functions and optimizing filter parameters based on specific application requirements.关键词
FIR数字滤波器/窗函数法/线性相位/频率响应/性能权衡Key words
FIR Digital Filter/Window Function Method/Linear Phase/Frequency Response/Performance Trade-offs引用本文复制引用
刘婧,李文学.FIR滤波器设计中窗函数的选择与性能权衡研究[EB/OL].(2025-12-29)[2025-12-30].http://www.paper.edu.cn/releasepaper/content/202512-42.学科分类
电子电路
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