This paper presents a new state-space method for spectral estimation that performs decimation by any factor and it is based on Singular Value Decomposition in order to estimate frequency, damping factor, amplitude and phase of complex damped sinusoids in the presence of noise. The new method, called DESE D, makes use of the full set of data and brings further apart the poles under consideration, while it imposes almost no constraints to the dimensions of the Hankel matrix, as decimation increases. It is compared against two previously proposed techniques for spectral estimation (along with derived decimative versions), that lie among the most promising methods in the field of spectroscopy, where accuracy of parameter estimation is of utmost importance. Moreover, it is compared against a state-of-the-art purely decimative method proposed in literature. Experiments performed on simulated NMR signals prove the new method to be more robust, especially for low signal to noise ratio.