Frequency Estimation Using Pisarenko, MUSIC, and ESPRIT Methods with Algorithm Implementation

This software performs frequency estimation using three advanced spectral analysis techniques: Pisarenko's method, MUSIC algorithm, and ESPRIT method. The Pisarenko method, widely applied in signal processing for frequency estimation, operates by constructing an autocorrelation matrix from input signals and extracting frequency information through eigen decomposition - typically implemented using MATLAB's eig() function or equivalent linear algebra libraries. The MUSIC (Multiple Signal Classification) method employs eigenvector decomposition of the covariance matrix to create a noise subspace, then identifies frequencies by finding peaks in the pseudospectrum. Code implementation generally involves steps like covariance matrix calculation, eigenvalue decomposition, and spectral peak searching through root-MUSIC or spectral MUSIC variations. ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) achieves high-resolution frequency estimation through rotational invariance properties in signal subspaces. Implementation typically requires matrix pencil formation, singular value decomposition (SVD) for subspace separation, and parameter extraction from phase information of eigenvalues. The integration of these three methods enables the software to provide robust frequency estimation across different signal-to-noise conditions, with Pisarenko handling basic frequency detection, MUSIC offering improved resolution, and ESPRIT delivering high-accuracy parameter estimation through advanced matrix computation techniques.