Oversampling in Shift-Invariant Spaces with a Rational Sampling Period Articles uri icon

publication date

  • September 2009

start page

  • 3442

end page

  • 3449

issue

  • 9

volume

  • 57

international standard serial number (ISSN)

  • 1053-587X

electronic international standard serial number (EISSN)

  • 1941-0476

abstract

  • It is well known that, under appropriate hypotheses, a sampling formula allows us to recover any function in a principal shift-invariant space from its samples taken with sampling period one. Whenever the generator of the shift-invariant space satisfiesthe Strang&-Fix conditions of order , this formula also provides an approximation scheme of order valid for smooth functions.In this paper we obtain sampling formulas sharing the same features by using a rational sampling period less than one. With the use of this oversampling technique, there is not one but an infinite number of sampling formulas. Whenever the generator has compact support, among these formulas it is possible to find one whose associated reconstruction functions have also compact support.