MATLAB Implementation of Prony Signal Processing Method

The provided MATLAB code implements the Prony method for signal processing, which specializes in parameter estimation of exponential signals within time series data. The implementation includes key algorithmic steps such as: constructing the Hankel matrix from input data, solving the linear prediction equations using matrix operations, calculating the roots of the characteristic polynomial through MATLAB's roots() function, and determining signal amplitudes via least-squares fitting. The code demonstrates how to extract complex exponentials from noisy measurements by employing singular value decomposition (SVD) for robust solution of linear systems. This approach enables accurate identification of signal frequencies, damping factors, and amplitudes, making it particularly valuable for applications in vibration analysis, power systems, and biomedical signal processing. The implementation includes error handling and validation checks to ensure reliable performance with various input data types.