Fundamental frequency estimation from the highest order coefficient of a polynomial

This paper presents a new method for the estimation of the fundamental frequency of a periodic signal. It uses the fact that several multitone frequency estimators end up finding the roots of a complex polynomial and that the highest order coefficient of this polynomial is the product of all the roots. The approach requiring complex data, it uses a DFT-based multitone frequency estimator and the resulting estimations have variance close to the Cramer-Rao Bound. A reduced-order version is also presented which can provide estimation that can be more accurate than the complete order method with a very low computational complexity.