Implementation of Wavelet Denoising and Adaptive Filtering for Input Signals Using MATLAB

This implementation demonstrates wavelet denoising and adaptive filtering of input signals using MATLAB. The process begins with wavelet decomposition of the input signal using functions like wavedec() or dwt(), which separates the signal into approximation and detail coefficients. For denoising, thresholding techniques (such as soft or hard thresholding) are applied to the wavelet coefficients using wthresh() and wden() functions to remove noise components while preserving important signal features.

Following denoising, adaptive filtering algorithms like LMS (Least Mean Squares) or RLS (Recursive Least Squares) are implemented using MATLAB's adaptfilt package or custom functions. The adaptive filter continuously adjusts its coefficients based on the error signal between the filtered output and desired response, effectively tracking signal variations and further improving signal quality.

This combined approach yields a cleaner, smoother signal with enhanced signal-to-noise ratio. Key implementation considerations include selecting appropriate wavelet types (Daubechies, Symlets), decomposition levels, threshold selection methods (universal, minimax), and adaptive filter parameters (step size, filter length) based on specific signal characteristics.