MATLAB Implementation of MUSIC Algorithm for Spectral Estimation

This article explores the implementation of the MUSIC algorithm in MATLAB for spectral estimation. We begin by introducing the fundamental principles of the MUSIC algorithm, which operates through eigenvalue decomposition of the covariance matrix to separate signal and noise subspaces. The algorithm's application in music spectral estimation is then discussed in detail, focusing on its high-resolution capabilities for frequency detection. Next, we describe the MATLAB implementation methodology, covering key functions such as cov() for covariance matrix calculation, eig() for eigenvalue decomposition, and peak detection techniques for spectrum analysis. The program structure follows a systematic workflow: data preprocessing, covariance matrix construction, subspace decomposition, spectral function calculation, and peak identification. Finally, we demonstrate practical usage through a concrete example involving synthetic music signals, showing how to configure parameters like sensor array geometry and snapshot numbers. The performance evaluation discusses the algorithm's advantages in resolution and limitations in scenarios with coherent sources or limited snapshots. This article aims to provide both theoretical insights and practical implementation guidelines to help readers effectively apply the MUSIC algorithm in spectral estimation tasks.