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Title: Uncertainty principles for linear and quadratic time-frequency representations
Authors: LI JIAWEN
Keywords: Uncertainty principles, time-frequency representations, signal recovery
Issue Date: 23-Feb-2008
Citation: LI JIAWEN (2008-02-23). Uncertainty principles for linear and quadratic time-frequency representations. ScholarBank@NUS Repository.
Abstract: Various uncertainty principles for linear and sesquilinear operators are studied. These uncertainty principles are classified into three classes, namely, concentration type, Benedicks type and Heisenberg type. For uncertainty principles of concentration type, general uncertainty principles for operators on Hilbert spaces are given. Consequences are derived, including uncertainty principles for integral operators between measure spaces and for frames in Hilbert spaces, which in turn give rise to uncertainty principles for the short-time Fourier transform, continuous wavelet transform, Wigner distribution, ambiguity function, Gabor frames, wavelet frames and frames in reproducing kernel Hilbert spaces. Uncertainty principles of Benedicks type have interesting ramifications in signal recovery. In particular, a stronger version of Donoho and Stark's signal recovery result to obtain missing segments of a bandlimited function is given. Lastly, uncertainty principles for the short-time Fourier transform, cross-ambiguity function and cross-Wigner distribution that are in the same spirit as the classical Heisenberg inequality are studied.
Appears in Collections:Master's Theses (Open)

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