Simulation of Various Linear Predictive Filters Using LMS Algorithm

In this study, we conducted simulations of various linear predictive filters using the LMS (Least Mean Squares) algorithm. The implementation leverages iterative weight adaptation through the formula w(n+1) = w(n) + μ·e(n)·x(n), where μ represents the step size, e(n) denotes the error signal, and x(n) is the input vector. Experimental results confirm the algorithm's high efficiency in convergence speed and computational simplicity, effectively reducing hardware resource requirements. Furthermore, we investigated the algorithm's applicability across different scenarios including noise cancellation and system identification, analyzing parameters such as filter length and step size selection. Optimization suggestions were proposed incorporating variable step-size techniques and stability-boundary calculations. These findings provide deeper insights into the LMS algorithm's advantages in real-time signal processing applications, offering valuable references for advancing adaptive filter technologies in embedded systems and DSP implementations.