Oversampling and Reconstruction Functions with Compact Support Articles uri icon

publication date

  • May 2009

start page

  • 245

end page

  • 253

issue

  • 2

volume

  • 227

International Standard Serial Number (ISSN)

  • 0377-0427

Electronic International Standard Serial Number (EISSN)

  • 1879-1778

abstract

  • Assume that a sequence of samples of a filtered version of a function in a shift-invariant space is given. This paper deals with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. This is done in the light of the generalized sampling theory by using the oversampling technique. A necessary and sufficient condition is given in terms of the Smith canonical form of a polynomial matrix. Finally, we prove that the aforesaid oversampled formulas provide nice approximation schemes with respect to the uniform norm.