MATLAB Implementation of LMS and RLS Adaptive Filter Algorithms

The following program implements both LMS and RLS adaptive filter algorithms using MATLAB software, characterized by concise and clear implementation rather than complex code structure. First, we define an input signal and add a set of noise components to it. The implementation utilizes a for loop structure to handle the iterative nature of adaptive filtering algorithms, where each iteration updates the filter coefficients based on the error signal. This approach demonstrates the core mathematical operations of both LMS (using gradient descent for coefficient updates) and RLS (employing recursive matrix inversion for optimal weight adaptation) algorithms. Through the application of these adaptive filters, we can effectively remove noise components and significantly improve signal quality by continuously adapting to the changing signal characteristics. The code structure efficiently handles real-time processing requirements while maintaining computational efficiency through optimized matrix operations and proper memory management.