Improved method for parameter estimation of complex sinusoids in noise

Using the theory of resultants/subresultants (inner determinants), a set of necessary conditions as well as another set of necessary conditions as well as another set of necessary and sufficient conditions, which are nonlinear functions of the polynomial coefficients, are obtained for all its roots to lie on the unit circle and be distinct from each other. The results have potential for improvement over previous methods for estimating parameters of sinusoids in noise where the constraints imposed provide only necessary conditions and are linearly related to the polynomial coefficients.