Coherence Spectrum Estimation From Nonuniformly Sampled Sequences

Magnitude squared coherence (MSC) is a useful bivariate spectral measure that finds application in a wide variety of fields. In this paper, we develop a nonparametric Capon-based MSC estimator that utilizes a segmented reformulation of the recently introduced iterative adaptive approach (IAA) to provide high resolution MSC spectrum estimates. The proposed estimator, termed segmented-IAA-MSC (or SIAA-MSC, for short), allows for unevenly sampled data as well as for sequences with arbitrarily missing samples. The estimator first uses segmented-IAA to find accurate estimates of the auto- and cross-covariance matrices of the given sequences. These estimates are then used in a Capon-based MSC estimator reformulated to allow for nonuniformly sampled sequences. To achieve higher statistical accuracy, the estimation problem is formulated so as to allow for overlapped segmentation of the available data. The proposed SIAA-MSC estimator is found to yield improved estimates as compared to the more commonly used least squares Fourier transform (LSFT) based MSC estimator.