Frequency Estimation of Complex Sinusoids with White Noise Using ESPRIT Algorithm

Using the ESPRIT algorithm to estimate the frequency of complex sinusoidal signals with additive white noise, where parameter f outputs the estimated frequency value of the sinusoidal component. The ESPRIT algorithm is a signal subspace-based frequency estimation method that extracts frequency information by exploiting the signal's eigenvector subspace. In practical implementation, ESPRIT operates by first constructing a Hankel matrix from the input signal, then performing singular value decomposition (SVD) to separate signal and noise subspaces. The key computational step involves solving a generalized eigenvalue problem to obtain rotational operators that directly yield frequency estimates. When estimating frequencies of complex sinusoids with white noise, the algorithm effectively suppresses noise interference by leveraging the orthogonality between signal and noise subspaces, thereby improving frequency estimation accuracy. The core MATLAB implementation typically involves functions like 'svd' for matrix decomposition and 'eig' for eigenvalue calculation. Consequently, the ESPRIT algorithm provides more precise signal frequency estimation results, enabling better understanding and analysis of complex sinusoidal signals with white noise characteristics. The algorithm's performance can be further optimized through proper selection of model order and matrix dimensions based on signal-to-noise ratio considerations.