Evaluation of Adaptive Filtering Algorithms in Signal Denoising: Insights from Simulation and Algorithmic Enhancement

Signal denoising is an important research direction in the field of signal processing, with widespread applications in communication, audio processing, medical signal analysis, and other areas. With the development of technology, traditional noise reduction methods are gradually facing bottlenecks in efficiency and accuracy, especially in dynamically changing noise environments. Adaptive filtering algorithms have become effective tools for solving noise elimination problems due to their ability to adjust filter parameters in real time based on the characteristics of the input signal. However, classical adaptive algorithms, such as Least Mean Square (LMS) and Normalized Least Mean Square (NLMS) algorithms, despite their success in many applications, still face issues such as slow convergence and insufficient performance when handling different types of noise. This study aims to explore the application of adaptive filtering algorithms in signal denoising, particularly those based on second-order statistics, evaluate their performance in different noise environments, and optimize their enhancement. Initially, simulations were undertaken to implement the LMS, NLMS, and second-order statistics-based adaptive filtering algorithms for noise removal experiments. These experiments employed various noise power levels and signal types to assess the performance of each algorithm, focusing on metrics such as Signal-to-Noise Ratio (SNR), Mean Squared Error (MSE), and the convergence speed of filter parameters. The research results show that the adaptive filtering algorithm based on second-order statistics has significant advantages over LMS and NLMS algorithms in various noise environments, especially in cases of higher noise power, where its denoising effect is more significant, and the convergence speed is also faster. Additionally, to address the computational complexity of the algorithm, this study proposes a simplification strategy to optimize the practical application performance of the algorithm.