This paper presents a new state-space method for spectral estimation based on a companion matrix technique in order to estimate frequency, damping factor, amplitude and phase of exponential sinusoids. The new method, called CSE, is compared against a previously proposed method called HTLS which is based on the use of total least squares. The latter lies among the most promising methods in the field of spectroscopy where accuracy of parameter estimation is of utmost importance. Experiments performed on a simulated NMR signal prove CSE to be more robust in terms of failure rate, especially for low signal to noise ratio.