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

Samplings with the Clifford algebra setting
 English Abstract

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Sampling is very important and widely used in various fields. The fundamental theorem in sampling is Shannon’s sampling theorem (see [1]), which deals with bandlimited functions that satisfy the Nyquist condition. Two cases are given in Natterer (2001): one is the sampling theorem when the Nyquist condition is oversatisfied; another is the sampling error and remarks when the Nyquist condition is not satisfied. Efforts have been made to generalize Shannon’s sampling theorem in the Clifford algebra setting. In this thesis, we attempt to present the sampling results of the two cases above in Clifford analysis. All of these conclusions are based on the generalized sinc function in [3] and the corresponding PaleyWiener Theorem (see [4]) in R n 1 . The sampling theorem when the Nyquist condition is oversatisfied is firstly discussed in this thesis. We generalize the sampling theorem from ndimension to (n+1)real variables in Clifford analysis. The significance of this theorem is the formula in it converges much faster than the sinc series. Secondly, we research on the sampling error formula in Clifford analysis when the Nyquist condition is not satisfied. Remarks are also included.
 Issue date

2013.
 Author

Zhao, Hai Lin
 Faculty

Faculty of Science and Technology
 Department

Department of Mathematics
 Degree

M.Sc.
 Subject

Clifford algebras
Functional analysis
Mathematical physics
 Supervisor

Qian, Tao
 Files In This Item
 Location
 1/F Zone C
 Library URL
 991004677839706306