摘要
信号去噪是现代信息处理领域中的关键问题，尤其在复杂噪声环境下，如何有效提取目标信号成为研究热点。本文针对传统滤波方法在非平稳信号处理中适应性不足的问题，提出了一种基于自适应滤波的信号去噪技术。该方法通过引入改进的自适应算法，结合时变特性分析，实现了对动态噪声环境的高效应对。研究首先从理论层面探讨了自适应滤波器的工作原理及其在信号分离中的应用潜力，并设计了一种融合小波变换与自适应滤波的混合模型，以提升去噪精度和鲁棒性。实验部分采用多种典型噪声类型进行验证，结果表明，所提方法在信噪比提升、均方误差降低以及边缘特征保留等方面均表现出显著优势。与传统固定参数滤波器相比，该方法能够根据输入信号的变化自动调整滤波参数，从而更好地适应实际应用场景。此外，本文还提出了基于自适应步长优化的改进策略，进一步提高了算法收敛速度和稳定性。研究表明，该技术不仅适用于一维信号处理，还可扩展至多维数据领域，为后续相关研究提供了新的思路。总体而言，本研究的主要贡献在于提出了一种兼具灵活性和高效性的信号去噪方案，为解决复杂噪声环境下的信号处理难题提供了有力支持。
关键词：自适应滤波；信号去噪；时变特性分析
Abstract
Signal denoising is a critical issue in modern information processing, particularly in complex noise environments where the effective extraction of target signals has become a research hotspot. In response to the limitations of traditional filtering methods in handling non-stationary signals, this study proposes an adaptive filtering-based signal denoising technique. By incorporating an improved adaptive algorithm and analyzing time-varying characteristics, the method achieves efficient adaptation to dynamic noise conditions. The research initially explores the working principles of adaptive filters from a theoretical perspective and evaluates their potential applications in signal separation. A hybrid model integrating wavelet transform with adaptive filtering is then designed to enhance denoising accuracy and robustness. In the experimental section, various typical noise types are employed for validation, and the results demonstrate that the proposed method exhibits significant advantages in terms of signal-to-noise ratio improvement, mean square error reduction, and edge feature preservation. Compared with traditional fixed-parameter filters, this approach can automatically adjust filtering parameters according to variations in input signals, thereby better accommodating practical application scenarios. Furthermore, an improved strategy based on adaptive step-size optimization is introduced, which enhances the convergence speed and stability of the algorithm. The study reveals that this technology is not only applicable to one-dimensional signal processing but can also be extended to multidimensional data domains, providing new insights for subsequent related research. Overall, the primary contribution of this research lies in proposing a signal denoising scheme that combines flexibility and efficiency, offering strong support for addressing signal processing challenges in complex noise environments.
Keywords：Adaptive Filtering; Signal Denoising; Time-Varying Characteristics Analysis
目 录
摘要 I
Abstract II
一、绪论 1
(一) 研究背景与意义 1
(二) 自适应滤波去噪技术的研究现状 1
(三) 本文研究方法概述 2
二、自适应滤波基础理论 2
(一) 自适应滤波的基本原理 2
(二) 常见自适应滤波算法分析 3
(三) 自适应滤波器的性能评价指标 4
(四) 自适应滤波在信号处理中的应用 4
三、自适应滤波去噪的关键技术 5
(一) 噪声特性与信号模型构建 5
(二) 自适应步长调整策略研究 5
(三) 滤波收敛性与稳定性分析 6
(四) 非平稳信号的自适应去噪方法 6
四、实验验证与结果分析 7
(一) 实验设计与数据采集 7
(二) 不同算法的对比实验 8
(三) 实验结果分析与讨论 8
(四) 自适应滤波去噪的实际应用案例 9
结 论 10
参考文献 11
信号去噪是现代信息处理领域中的关键问题，尤其在复杂噪声环境下，如何有效提取目标信号成为研究热点。本文针对传统滤波方法在非平稳信号处理中适应性不足的问题，提出了一种基于自适应滤波的信号去噪技术。该方法通过引入改进的自适应算法，结合时变特性分析，实现了对动态噪声环境的高效应对。研究首先从理论层面探讨了自适应滤波器的工作原理及其在信号分离中的应用潜力，并设计了一种融合小波变换与自适应滤波的混合模型，以提升去噪精度和鲁棒性。实验部分采用多种典型噪声类型进行验证，结果表明，所提方法在信噪比提升、均方误差降低以及边缘特征保留等方面均表现出显著优势。与传统固定参数滤波器相比，该方法能够根据输入信号的变化自动调整滤波参数，从而更好地适应实际应用场景。此外，本文还提出了基于自适应步长优化的改进策略，进一步提高了算法收敛速度和稳定性。研究表明，该技术不仅适用于一维信号处理，还可扩展至多维数据领域，为后续相关研究提供了新的思路。总体而言，本研究的主要贡献在于提出了一种兼具灵活性和高效性的信号去噪方案，为解决复杂噪声环境下的信号处理难题提供了有力支持。
关键词：自适应滤波；信号去噪；时变特性分析
Abstract
Signal denoising is a critical issue in modern information processing, particularly in complex noise environments where the effective extraction of target signals has become a research hotspot. In response to the limitations of traditional filtering methods in handling non-stationary signals, this study proposes an adaptive filtering-based signal denoising technique. By incorporating an improved adaptive algorithm and analyzing time-varying characteristics, the method achieves efficient adaptation to dynamic noise conditions. The research initially explores the working principles of adaptive filters from a theoretical perspective and evaluates their potential applications in signal separation. A hybrid model integrating wavelet transform with adaptive filtering is then designed to enhance denoising accuracy and robustness. In the experimental section, various typical noise types are employed for validation, and the results demonstrate that the proposed method exhibits significant advantages in terms of signal-to-noise ratio improvement, mean square error reduction, and edge feature preservation. Compared with traditional fixed-parameter filters, this approach can automatically adjust filtering parameters according to variations in input signals, thereby better accommodating practical application scenarios. Furthermore, an improved strategy based on adaptive step-size optimization is introduced, which enhances the convergence speed and stability of the algorithm. The study reveals that this technology is not only applicable to one-dimensional signal processing but can also be extended to multidimensional data domains, providing new insights for subsequent related research. Overall, the primary contribution of this research lies in proposing a signal denoising scheme that combines flexibility and efficiency, offering strong support for addressing signal processing challenges in complex noise environments.
Keywords：Adaptive Filtering; Signal Denoising; Time-Varying Characteristics Analysis
目 录
摘要 I
Abstract II
一、绪论 1
(一) 研究背景与意义 1
(二) 自适应滤波去噪技术的研究现状 1
(三) 本文研究方法概述 2
二、自适应滤波基础理论 2
(一) 自适应滤波的基本原理 2
(二) 常见自适应滤波算法分析 3
(三) 自适应滤波器的性能评价指标 4
(四) 自适应滤波在信号处理中的应用 4
三、自适应滤波去噪的关键技术 5
(一) 噪声特性与信号模型构建 5
(二) 自适应步长调整策略研究 5
(三) 滤波收敛性与稳定性分析 6
(四) 非平稳信号的自适应去噪方法 6
四、实验验证与结果分析 7
(一) 实验设计与数据采集 7
(二) 不同算法的对比实验 8
(三) 实验结果分析与讨论 8
(四) 自适应滤波去噪的实际应用案例 9
结 论 10
参考文献 11
