UM ETheses Collection (澳門大學電子學位論文庫)
 Title

The generalized sampling expansions associated with quaternion Fourier transform
 English Abstract

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The WhittakerShannonKotel’nikov (WSK) sampling theorem provides a reconstruction formula for the PaleyWiener class of bandlimited functions. In this thesis, we would like to develop the sampling expansions of quaternionvalued functions in two different directions. On the one hand, we investigate some important properties of quaternion Fourier transform (QFT) such as inversion, Plancherel theorem, convolution theorem. We present the Papoulislike generalized sampling expansion associated with QFT by using generalized translation and convolution. It is shown that a σbandlimited function in QFT sense can be reconstructed in terms of the samples of output functions of M linear systems based on QFT. Some examples are presented to illustrate the result. On the other hand, a generalization of the WSK sampling theorem is extended by using the theory of quaternion reproducing kernel Hilbert space. Also, we present a novel approach, based on the quaternion reproducing kernel Hilbert space, to the generalization of the prolate spheroidal wave functions. This generalization is then employed to obtain a sampling formula for a general class of bandlimited functions. A special case of our result is to show that the 2D generalized prolate spheroidal wave functions obtained by Slepian can also be used to achieve a sampling series for functions bandlimited to the cube. The solutions to the energy concentration problems in quaternion Hilbert space with QFT are also investigated.
 Issue date

2015
 Author

Cheng, Dong
 Faculty

Faculty of Science and Technology
 Degree

M.Sc.
 Subject

Fourier analysis
Quaternions
Mathematics  Department of Mathematics
 Supervisor

Kou, Kit Ian
 Files In This Item
 Location
 1/F Zone C
 Library URL
 991000746759706306