This paper presents a matrix pencil method for estimating the parameters (frequencies and damping factors) of exponentially damped or undamped sinusoids in noise. The method is compared to the polynomial method (SVD-Prony method), showing that both are special cases of a matrix prediction approach. However, the matrix pencil method is more efficient in computation and less restrictive about signal poles. Perturbation analysis and simulation show that the matrix pencil method is less sensitive to noise than the polynomial method, especially for signals with unknown damping factors. The matrix pencil method uses the structure of a matrix pencil of the underlying signal, rather than the structure of prediction equations. It is based on the property that the generalized eigenvalues of the matrix pencil are the same as the eigenvalues of a certain matrix derived from the data. The method involves constructing two matrices, X0 and X1, from the data sequence, and then solving a generalized eigenvalue problem to estimate the signal parameters. The matrix pencil method is compared to the polynomial method in terms of computational efficiency and noise sensitivity. The polynomial method requires SVD of a data matrix and finding roots of a polynomial, while the matrix pencil method requires SVD of the same data matrix and computing eigenvalues of a smaller matrix. The matrix pencil method is more efficient in computation and less restrictive about signal poles. The paper also discusses the noise sensitivity of the matrix pencil method. It shows that the matrix pencil method is less sensitive to noise than the polynomial method, especially for signals with unknown damping factors. The method is also compared to the FB (forward-backward) versions of the polynomial and matrix pencil methods, which are more robust to noise for undamped signals. The paper concludes that the matrix pencil method is a more efficient and less sensitive method for estimating the parameters of exponentially damped or undamped sinusoids in noise compared to the polynomial method. The Cramer-Rao bound is also discussed, showing that the matrix pencil method has a lower bound for the variance of the estimated parameters.This paper presents a matrix pencil method for estimating the parameters (frequencies and damping factors) of exponentially damped or undamped sinusoids in noise. The method is compared to the polynomial method (SVD-Prony method), showing that both are special cases of a matrix prediction approach. However, the matrix pencil method is more efficient in computation and less restrictive about signal poles. Perturbation analysis and simulation show that the matrix pencil method is less sensitive to noise than the polynomial method, especially for signals with unknown damping factors. The matrix pencil method uses the structure of a matrix pencil of the underlying signal, rather than the structure of prediction equations. It is based on the property that the generalized eigenvalues of the matrix pencil are the same as the eigenvalues of a certain matrix derived from the data. The method involves constructing two matrices, X0 and X1, from the data sequence, and then solving a generalized eigenvalue problem to estimate the signal parameters. The matrix pencil method is compared to the polynomial method in terms of computational efficiency and noise sensitivity. The polynomial method requires SVD of a data matrix and finding roots of a polynomial, while the matrix pencil method requires SVD of the same data matrix and computing eigenvalues of a smaller matrix. The matrix pencil method is more efficient in computation and less restrictive about signal poles. The paper also discusses the noise sensitivity of the matrix pencil method. It shows that the matrix pencil method is less sensitive to noise than the polynomial method, especially for signals with unknown damping factors. The method is also compared to the FB (forward-backward) versions of the polynomial and matrix pencil methods, which are more robust to noise for undamped signals. The paper concludes that the matrix pencil method is a more efficient and less sensitive method for estimating the parameters of exponentially damped or undamped sinusoids in noise compared to the polynomial method. The Cramer-Rao bound is also discussed, showing that the matrix pencil method has a lower bound for the variance of the estimated parameters.