Signal Frequency Estimation Using ESPRIT Algorithm with MATLAB Implementation

This document presents my personally developed MATLAB code for signal frequency estimation using the ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm. The implementation features efficient matrix manipulation through Hankel matrix construction for signal subspace estimation, followed by rotational invariance property exploitation using eigenvalue decomposition of correlated matrices. The code incorporates automatic order detection and includes noise resilience mechanisms through proper subspace separation. Key algorithmic components include: - Covariance matrix computation for signal characterization - Signal subspace identification via singular value decomposition (SVD) - Rotational invariance implementation using matrix pencil method - Frequency extraction through eigenvalue angle calculation After extensive debugging and optimization cycles, the code achieves high computational efficiency while maintaining estimation accuracy. The implementation handles complex-valued signals and provides configurable parameters for various signal-to-noise ratio conditions. This ready-to-use solution serves as a practical tool for both academic research and real-world applications involving spectral analysis and signal processing. I hope this carefully crafted implementation proves valuable for your frequency estimation tasks and provides insight into ESPRIT algorithm's practical implementation nuances.