IIR, FIR, LMS, NLMS Algorithms Implementation

This document describes MATLAB M-code implementations of IIR, FIR, LMS, and NLMS algorithms. The code provides practical implementations for various digital signal processing scenarios, including detailed explanations of each algorithm's characteristics and applications. For instance, IIR filters are ideal for high-pass or low-pass filtering applications due to their recursive structure and efficient implementation using fewer coefficients, though they may suffer from stability issues that require careful pole placement. FIR filters, implemented using non-recursive structures with symmetric coefficient arrangements, avoid stability problems entirely but require more computational resources due to their longer filter lengths. The LMS algorithm serves primarily for system identification and adaptive filtering applications, utilizing gradient descent optimization with a fixed step-size parameter for weight updates. The NLMS algorithm enhances LMS performance by normalizing the step-size with the input signal power, resulting in faster convergence and improved stability. The M-code implementation includes essential functions like filter design (butter, fir1), adaptive filtering routines, and convergence analysis tools, providing comprehensive resources for signal processing and system identification applications.