Research on Music High-Order Spectral Analysis Algorithms

This research focuses on high-order spectral analysis algorithms for music signals, incorporating signal dimension estimation through the MDL criterion. The study explores advanced spectral characteristics in music using sophisticated mathematical and statistical methods, with particular emphasis on their applications in music analysis. Algorithm implementation involves computing higher-order cumulants and spectra to capture phase relationships and non-Gaussian characteristics beyond conventional power spectrum analysis. The MDL criterion implementation requires developing information-theoretic models for optimal parameter selection in subspace methods like MUSIC (Multiple Signal Classification). Key technical components include: covariance matrix estimation, eigenvalue decomposition for signal subspace identification, and model order selection using information criteria. The research aims to propose novel algorithms and techniques to better understand musical structures and features, contributing to both academic music research and music industry applications through improved signal processing methodologies.