Wavelet Signal Denoising Examples

This example demonstrates wavelet-based signal denoising techniques. We explore three distinct denoising methodologies: default threshold denoising, forced denoising, and soft threshold denoising. These approaches effectively remove noise components from signals while enhancing overall signal quality. Default threshold denoising employs a straightforward implementation using predefined threshold values (typically calculated via wavelet coefficient analysis) to eliminate noise components. This method can be implemented using MATLAB's wden function with 'sqtwolog' threshold selection rule. Forced denoising provides more precise noise removal by adapting threshold parameters based on specific signal characteristics. This approach often involves level-dependent thresholding where different thresholds are applied to various wavelet decomposition levels, effectively targeting noise while preserving signal features through careful coefficient selection. Soft threshold denoising implements a nonlinear shrinkage approach where wavelet coefficients below a certain threshold are smoothly attenuated rather than completely eliminated. This method maintains better preservation of signal details through continuous thresholding functions, typically implemented using the 's' threshold type in wavelet denoising functions. The soft thresholding operation can be mathematically represented as: sign(x)·max(0, |x|-threshold). By comparing these three denoising strategies, engineers can select optimal approaches based on specific signal characteristics and application requirements to achieve enhanced signal quality with appropriate noise reduction.