On the Reconstruction of Gapped Sinusoidal Data

The problem of estimating a spectral representation of damped sinusoidal signals from a gapped data set is of considerable interest in several applications. In this paper, we propose a filterbank approach to provide such an estimate, by first reconstructing the missing data samples assuming that the spectral content of the missing data is similar to that of the available samples, and then forming a spectral representation of the reconstructed data set as a function of frequency and damping. Numerical examples illustrate the benefits of the proposed estimator as compared to currently available methods.