Spectral Analysis of Gapped or Missing Data

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Jian LiSpectral Analysis of Gapped or Missing DataThis research focuses on the spectral analysis of gapped or incomplete data sequences. The gapped or missing data problem usually arises when contiguous data measurements for a long time are hard to obtain or the measurements during some intervals are not useful due to strong interference or jamming and must be discarded. Spectral analysis of gapped or incomplete data sequences holds promise to advance many fields including astronomy, communications, medical imaging, radar, and underwater acoustics.This research involves the development and application of efficient and robust spectral analysis algorithms for incomplete data sequences. The goals of this research are to devise and evaluate statistically sound and mathematically solid spectral analysis methods for various applications that involve the spectral analysis of gapped or incomplete data sequences, to gain both practical and theoretical insights into the algorithm properties including accuracy, resolution, convergence, and computational complexity, and to understand the impacts of large gaps or large numbers of missing data samples on the algorithm design. It is anticipated that the results of this study will significantly impact the advances of many practical applications.