ESPRIT Algorithm MATLAB Implementation with Code Examples

This document presents a detailed MATLAB implementation of the ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm. The ESPRIT algorithm is a high-performance frequency estimation method extensively applied in radar systems, sonar technology, and wireless communications. The core methodology involves decomposing complex signals into constituent sinusoids through subspace decomposition techniques, followed by a two-stage parameter estimation process that leverages rotational invariance properties between signal subspaces. Key implementation aspects covered in the MATLAB code include: - Signal subspace estimation using singular value decomposition (SVD) or eigenvalue decomposition - Construction of Hankel/Toeplitz matrices for signal covariance estimation - Automated model order selection based on information criteria (AIC/MDL) - Resolution of rotational invariance equations through least-squares solutions The algorithm demonstrates superior performance characteristics including high spectral resolution accuracy, robustness against additive white Gaussian noise, and computational efficiency compared to conventional FFT-based methods. The provided MATLAB implementation features modular functions for data preprocessing, covariance matrix computation, and parameter extraction, enabling users to validate algorithm performance with customizable signal-to-noise ratios and multiple sinusoid components. This implementation serves as an essential toolkit for researchers and engineers developing advanced signal processing applications, offering both educational value and practical deployment capabilities.