Frequency Estimation Using Pisarenko Harmonic Estimation Method

This document presents frequency estimation techniques using Pisarenko harmonic estimation, MUSIC algorithm, and ESPRIT algorithm applied to three sinusoidal signals contaminated with additive white Gaussian noise. The accompanying code includes MATLAB implementations with comprehensive documentation. These signal processing algorithms are widely used for accurate frequency estimation of signal sources. The Pisarenko harmonic estimation method performs frequency estimation through eigenvalue decomposition of the signal's autocorrelation matrix, where the smallest eigenvalue corresponds to the noise subspace. The MUSIC algorithm employs spatial spectrum estimation to extract frequency information by constructing a noise subspace matrix and identifying spectral peaks. The ESPRIT algorithm leverages signal subspace characteristics for frequency estimation by utilizing the rotational invariance property of signal subspaces. Successful implementation requires mathematical foundations in linear algebra and programming skills, but the detailed code explanations provided in the attachments will enable users to understand and apply these algorithms effectively for frequency estimation tasks. Key MATLAB functions used include eig() for eigenvalue decomposition, svd() for singular value decomposition, and root() for polynomial solving in the Pisarenko implementation.