Sinusoids in white noise: A quadratic programming approach

We address the problem of the estimation and identification of real sinusoids in white Gaussian noise using a correlation-based method. We estimate a partial covariance sequence from the data and seek a representation of these new observations as a superposition of a small number of cosines chosen from a redundant basis and the white noise contribution. We propose to minimize a quadratic program in order to choose a parsimonious decomposition among the many that allow the reconstruction. We develop optimality conditions for the criterion that can be geometrically interpreted and present a dual criterion that has an appealing physical interpretation. Some simulated examples are also presented to show the excellent performance in resolution of the approach.