MATLAB Implementation of Stationary Wavelet Transform with Applications

The Stationary Wavelet Transform (SWT) is a fundamental technique in signal processing used to analyze frequency and temporal characteristics of signals. In MATLAB implementations, SWT can be employed for various applications such as signal denoising through the swt() function, which performs multilevel stationary wavelet decomposition. The transform works by decomposing signals into wavelet coefficients across different scales and frequency bands, enabling extraction of various frequency components for comprehensive signal analysis and processing. The algorithm maintains the same number of coefficients at each decomposition level by eliminating downsampling, making it shift-invariant compared to the discrete wavelet transform. Beyond denoising applications using thresholding techniques like wdencmp() or wthresh(), SWT finds extensive use in signal compression through coefficient thresholding, feature extraction for pattern recognition, and time-frequency analysis. Key MATLAB functions include swt() for forward transformation, iswt() for inverse transformation, and wdenoise() for denoising applications with customizable threshold rules.