摘 要
随着现代通信技术的快速发展，信号处理在提升通信系统性能方面的重要性日益凸显，而小波变换作为一种强大的数学工具，因其多分辨率分析特性，在非平稳信号处理中展现出独特优势。本研究以小波变换为核心，探讨其在通信信号去噪、压缩及特征提取中的应用，旨在解决传统方法在复杂环境下的不足。通过构建基于离散小波变换的信号处理模型，并结合实际通信场景进行实验验证，结果表明该方法能够显著提高信号的信噪比和传输效率，同时降低数据冗余。此外，本文提出了一种改进的小波阈值去噪算法，有效提升了弱信号环境下通信质量，为复杂通信系统的优化提供了新思路。研究的主要贡献在于将小波变换与通信需求深度融合，不仅拓展了小波理论的应用范围，还为未来通信技术的发展奠定了理论基础。
关键词：小波变换；信号处理；通信系统
Abstract
With the rapid development of modern communication technology, the importance of signal processing in enhancing the performance of communication systems has become increasingly prominent. As a powerful mathematical tool, wavelet transform demonstrates unique advantages in non-stationary signal processing due to its multi-resolution analysis characteristics. This study focuses on wavelet transform and explores its applications in communication signal denoising, compression, and feature extraction, aiming to address the limitations of traditional methods in complex environments. By constructing a signal processing model based on discrete wavelet transform and conducting experimental verification in practical communication scenarios, the results show that this approach can significantly improve the signal-to-noise ratio and transmission efficiency while reducing data redundancy. Furthermore, an improved wavelet threshold denoising algorithm is proposed, effectively enhancing communication quality in weak signal environments and providing new insights for optimizing complex communication systems. The primary contribution of this research lies in the deep integration of wavelet transform with communication requirements, not only expanding the application scope of wavelet theory but also laying a theoretical foundation for the future development of communication technologies.
Keywords: Wavelet Transform；Signal Processing；Communication System
目 录
引言 1
一、小波变换基础理论研究 1
（一）小波变换的基本概念 1
（二）小波变换的数学模型 2
（三）小波变换在信号处理中的优势 2
二、通信信号的小波分解与重构 3
（一）信号分解原理分析 3
（二）多分辨率分析方法应用 3
（三）信号重构算法设计 3
三、小波变换在通信噪声抑制中的应用 4
（一）噪声特性与小波阈值处理 4
（二）自适应去噪算法设计 4
（三）实验验证与性能评估 5
四、小波变换在数据压缩与传输中的优化 5
（一）数据压缩原理探讨 5
（二）基于小波的压缩算法实现 6
（三）传输效率提升策略研究 6
结 论 6
致 谢 8
参考文献 9
