摘 要：小波分析作为一种多尺度信号处理工具，近年来在去噪领域展现出显著优势。本文针对传统去噪方法在复杂信号处理中效果有限的问题，提出基于小波阈值的改进去噪算法。研究通过分析不同小波基函数对信号分解的影响，结合自适应阈值选取策略，优化了去噪过程中的细节保留与噪声抑制能力。实验采用多种典型信号进行验证，结果表明该方法在信噪比提升和均方误差降低方面较传统方法具有明显改进。此外，本文创新性地引入非均匀小波分解技术，有效解决了高频段信号去噪精度不足的难题。研究表明，所提方法不仅能够准确分离信号与噪声，还具备较强的普适性和鲁棒性，为实际工程应用提供了新思路。这一研究成果对推动小波分析在现代信号处理领域的深入应用具有重要意义。
关键词：小波阈值去噪；自适应阈值；非均匀小波分解；信噪比提升；高频段去噪精度
Research on Denoising Techniques in Signal Processing Using Wavelet Analysis
英文人名
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Abstract：Wavelet analysis, as a multiscale signal processing tool, has demonstrated significant advantages in the denoising field in recent years. In response to the limitations of traditional denoising methods in handling complex signals, this study proposes an improved denoising algorithm based on wavelet thresholding. By analyzing the impact of different wavelet basis functions on signal decomposition and incorporating an adaptive threshold selection strategy, the proposed method optimizes the balance between detail preservation and noise suppression during the denoising process. Experiments conducted using various typical signals confirm that this approach achieves noticeable improvements over conventional methods in terms of signal-to-noise ratio enhancement and reduction of mean square error. Furthermore, this paper innovatively introduces non-uniform wavelet decomposition technology, effectively addressing the challenge of insufficient denoising accuracy in high-frequency signal segments. The research findings indicate that the proposed method not only accurately separates signals from noise but also exhibits strong universality and robustness, providing new insights for practical engineering applications. This study contributes significantly to advancing the application of wavelet analysis in modern signal processing.
Keywords: Wavelet Threshold Denoising；Adaptive Threshold；Non-Uniform Wavelet Decomposition；Signal-To-Noise Ratio Enhancement；High-Frequency Band Denoising Accuracy
目 录
引言 1
一、小波分析基础理论 1
(一)小波变换基本概念 1
(二)多分辨率分析方法 2
(三)小波基函数选择策略 2
二、信号去噪原理与方法 3
(一)噪声类型及其特性 3
(二)小波阈值去噪原理 3
(三)自适应去噪算法设计 4
三、小波去噪关键技术研究 4
(一)阈值函数优化方法 4
(二)去噪参数选取准则 5
(三)多尺度分解技术应用 5
四、小波去噪的实际应用案例 6
(一)生物医学信号处理 6
(二)图像信号去噪分析 6
(三)工业信号噪声抑制 7
结论 7
参考文献 3
致谢 3
