The paper presents a study of the matrix pencil method for estimating parameters (frequencies and damping factors) of exponentially damped and/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. The paper also demonstrates that the matrix pencil method is less sensitive to noise than the polynomial method. A first-order perturbation analysis and simulation results support these findings. The Cramér-Rao bound for exponentially damped sinusoids is derived in Appendix A, revealing properties similar to those of both methods.The paper presents a study of the matrix pencil method for estimating parameters (frequencies and damping factors) of exponentially damped and/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. The paper also demonstrates that the matrix pencil method is less sensitive to noise than the polynomial method. A first-order perturbation analysis and simulation results support these findings. The Cramér-Rao bound for exponentially damped sinusoids is derived in Appendix A, revealing properties similar to those of both methods.