Implementation of Line Spectrum Enhancement Using LMS Algorithm and Adaptive Filtering

This article presents an adaptive line spectrum enhancement function implementation. The function utilizes the Least Mean Squares (LMS) algorithm and adaptive filtering techniques to achieve line spectrum enhancement. Our primary objective is to enhance single-frequency signals (with frequency f) that are contaminated by white noise characterized by mean mu and standard deviation sigma. The implementation involves a systematic signal analysis and processing workflow that includes: - Noise characterization and signal preprocessing - Adaptive filter design using LMS algorithm with adjustable step-size parameter - Real-time coefficient updating mechanism for optimal filter performance - Frequency-domain analysis for enhanced signal quality assessment The core algorithm employs a transversal filter structure where the filter coefficients are continuously adapted using the LMS update rule: w(n+1) = w(n) + μ·e(n)·x(n), where μ represents the convergence factor, e(n) is the error signal, and x(n) is the input vector. This methodology is not limited to single-frequency signals but can be effectively extended to handle various signal types including multi-frequency signals and complex waveforms. The implementation provides configurable parameters for filter length, adaptation rate, and noise threshold settings to accommodate different application scenarios. We hope this article offers valuable insights and practical approaches for researchers in related fields, while also serving as a useful reference for practical applications requiring robust signal enhancement solutions. The code architecture supports modular implementation with clear separation between signal input processing, adaptive filtering core, and enhanced output generation.