Volume 30, Issue 1
On a Class of Generalized Sampling Functions

Y. Wang

Anal. Theory Appl., 30 (2014), pp. 82-89

Published online: 2014-03

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  • Abstract

In this note, we discuss a class of so-called generalized sampling functions.These functions are defined to be the inverse Fourier transform of a family of piecewiseconstant functions that are either square integrable or Lebegue integrable on the realnumber line. They are in fact the generalization of the classic sinc function.Two approaches of constructing the generalized sampling functions are reviewed. Theirproperties such as cardinality, orthogonality, and decaying properties are discussed.The interactions of those functions and Hilbert transformer are also discussed.

  • Keywords

Generalized sampling function sinc function non-bandlimited signal sampling theorem Hilbert transform

  • AMS Subject Headings

41 42

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COPYRIGHT: © Global Science Press

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@Article{ATA-30-82, author = {Y. Wang}, title = {On a Class of Generalized Sampling Functions}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {1}, pages = {82--89}, abstract = {In this note, we discuss a class of so-called generalized sampling functions.These functions are defined to be the inverse Fourier transform of a family of piecewiseconstant functions that are either square integrable or Lebegue integrable on the realnumber line. They are in fact the generalization of the classic sinc function.Two approaches of constructing the generalized sampling functions are reviewed. Theirproperties such as cardinality, orthogonality, and decaying properties are discussed.The interactions of those functions and Hilbert transformer are also discussed.}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n1.5}, url = {http://global-sci.org/intro/article_detail/ata/4474.html} }
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