Spectral Analysis of Non-Uniformly Sampled Data: A New Approach Versus the Periodogram

We begin by revisiting the plain least-squares periodogram (LSP) for real-valued data. Then we introduce a new method for spectral analysis of non-uniformly sampled data by "iteratively weighting LSP", and we name the new method real-valued iterative adaptive approach (RIAA). LSP and RIAA are most suitable for data sequences with discrete spectra. For such type of data, we present a procedure to obtain a parametric spectral estimate, from the LSP or RIAA non-parametric estimate, by means of the Bayesian information criterion (BIC). We also discuss a possible strategy for designing the sampling pattern of future measurements. Several numerical examples are provided to illustrate the performance of our proposed approaches.