Hybrid Newton/Gauss-Newton algorithm for time-domain analysis of A/D converters

This brief describes a maximum-likelihood estimator for a sum of harmonically related sinewaves for characterizing analog-to-digital (A/D) converters. The frequency is estimated by means of the Newton method. For the iterations where singularity problems occur, the algorithm switches to the Gauss-Newton method combined with the singular value decomposition. The initial frequency accuracy required by this algorithm is determined and the algorithm is modified in order to converge to the global minimum, whatever the initial frequency uncertainty. Thus, one can use the frequencies of the signal generators to provide the starting value. Once the frequency is determined, the linear parameters of the model are estimated by solving a linear set of equations. It is shown through simulation and experimental results that the proposed algorithm is fast, accurate, and robust, with respect to the initial guess of the frequency.