An Abstraction of Shannon's Sampling Theorem

11 References
  • HONDA Ikuji
    Dept. of Mathematics, Faculty of Science and Technology, Keio University

Bibliographic Information

Other Title
  • 標本化定理の抽象化

Search this article

Description

We prove an abstract sampling theorem by studying the principle of original interpolation formula known as Shannon's sampling theorem. Let H_o a closed subspace in H &colone L^2(R) and say H_o signal space. Main aim of this paper is giving a necessary and sufficient condition for unique existence of a Riesz basis {S_n}(said a sampling basis) in and proving the abstract sampling theorem without band-limited assumption. We say {S_n}⊂H_o also a sequence of sampling functions. Based on the main result we also discuss about frequency domain and a coordinate transformation in the signal space. Then we are able to consider many known sampling theorems including Shannon's original, concrete examples of the abstract sampling theorem.

Journal

References(11)*help

See more

Keywords

Details 詳細情報について

  • CRID
    1570291227424163840
  • NII Article ID
    110003197168
  • NII Book ID
    AN10013083
  • Text Lang
    ja
  • Data Source
    • CiNii Articles

Report a problem

Back to top