Custom Singular Value Decomposition Noise Reduction Program

This article presents a custom Singular Value Decomposition (SVD) noise reduction program that implements dual functionality: noise elimination and frequency-based signal separation. The algorithm works by first constructing a Hankel matrix from the input signal, then performing SVD to decompose the matrix into singular values and vectors. The key implementation involves thresholding singular values where smaller values (typically representing noise) are truncated while preserving larger values corresponding to meaningful signal components. For frequency separation, the program utilizes the orthogonal property of SVD's U and V matrices to isolate different frequency components by grouping specific singular vectors. This approach allows researchers to analyze signal characteristics more effectively in frequency domains. The MATLAB-based implementation includes customizable parameters for threshold selection (hard/soft thresholding) and component grouping, making it adaptable to various signal types. Additional advantages include high customizability through adjustable threshold parameters and user-friendly interface design. The program finds broad applications across multiple domains including audio processing (speech enhancement), image processing (artifact removal), and biomedical engineering (ECG/EEG signal analysis). With its modular code structure featuring core functions like hankel_matrix(), svd_thresholding(), and component_reconstruction(), this SVD-based denoising tool provides researchers with practical capabilities for enhanced signal processing and data interpretation.