A Z-Test-Based Evaluation of a Least Mean Square Filter for Noise Reduction

This paper presents a comprehensive evaluation using a Z-test to assess the effectiveness of an adaptive Least Mean Squares (LMS) filter driven by the Steepest Descent Method (SDM). The study utilizes a male voice recording, captured in a controlled studio environment, to which persistent Gaussian noise was intentionally introduced, simulating real-world interference. All signal processing methods were implemented accordingly in MATLAB.version: 9.13.0 (R2022b), Natick, MA, USA: The MathWorks Inc.; 2022. The adaptive filter demonstrated a significant improvement of 20 dB in Signal-to-Noise Ratio (SNR) following the initial optimization of the filter parameter μ. To further assess the LMS filter’s performance, an empirical experiment was conducted with 30 young adults, aged between 20 and 30 years, who were tasked with qualitatively distinguishing between the clean and noise-corrupted signals (blind test). The quantitative analysis and statistical evaluation of the participants’ responses revealed that a significant majority, specifically 80%, were able to reliably identify the noise-affected and filtered signals. This outcome highlights the LMS filter’s potential—despite the slow convergence of the SDM—for enhancing signal clarity in noise-contaminated environments, thus validating its practical application in speech processing and noise reduction.