Estimation of Multiple Sinusoids by Parametric Filtering

Abstract

The problem of estimating the frequencies of multiple sinusoids from noisy observations is addressed in this paper. A parametric filtering approach, called the PF method, is proposed that leads to a consistent estimator of the AR representation of the sinusoidal signal, given the number of sinusoids. It is accomplished by using an iterative procedure to a fixed-point of the parametrized least squares estimator (from the filtered data) that comprises a contraction mapping in the vicinity of the true AR parameter. Employing appropriate filters, this method is able to achieve the accuracy of the nonlinear least squares estimator, with much less computational complexity and initialization requirement. It can also be implemented adaptively (recursively) in order to track time-varying frequencies. In this way, the PF method provides a flexible and efficient procedure of frequency estimation. An example of the AR filter is investigated in detail to illustrate the performance of the PF method.