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Title: Series expansions in cross-ambiguity functions
Authors: CHAN JIA LE
Keywords: cross-ambiguity functions; Gabor systems; Wigner and cross-Wigner distributions
Issue Date: 11-Feb-2009
Citation: CHAN JIA LE (2009-02-11). Series expansions in cross-ambiguity functions. ScholarBank@NUS Repository.
Abstract: Various expansions in ambiguity and cross-ambiguity functions are studied in this thesis. Using special well-known classes of functions (orthonormal bases, frames, Riesz bases and biorthogonal bases) as building blocks, series expansions in terms of ambiguity and cross-ambiguity functions are obtained and analyzed in detail, first for subspaces of $L^2(\real^2)$ before extending to the whole of $L^2(\real^2)$. A unitary map of fundamental importance is used extensively to break down the ambiguity and cross-ambiguity functions into their respective tensor products, which shows that the former possess similar properties as the functions used to construct them. Characterization of ambiguity functions is also studied, with specific focus on orthonormal bases for Paley-Wiener spaces and Gabor systems that are orthonormal bases or frames for $L^2(\real)$. In addition, Wigner and cross-Wigner distributions are developed and dealt with in the same manner as the case of the ambiguity and cross-ambiguity functions. Series expansions are useful for many practical applications, such as radar signal processing and TDOA and FDOA estimations.
Appears in Collections:Master's Theses (Open)

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