Doctor of Philosophy
Date of Defense
In data analysis and signal processing, the recovery of structured functions (in terms of frequencies and coefficients) with respect to certain basis functions from the given sampling values is a fundamental problem. The original Prony method is the main tool to solve this problem, which requires the equispaced sampling values.
In this dissertation, we use the equispaced sampling values in the frequency domain after the short time Fourier transform in order to reconstruct some signal expansions, such as the exponential expansions and the cosine expansions. In particular, we consider the case that the phase of the cosine expansion is quadratic. Moreover, we work on the expansion problem based on the eigenfunctions of some linear operators. In addition, when the signals contain two different models, we develop a method that separate the signals in single-models and then solve the problem. We also consider the situation that when some of the sampling values are corrupted.
Hussen, Abdulmtalb Mohamed, "Recover Data in Sparse Expansion Forms Modeled by Special Basis Functions" (2019). Dissertations. 896.