Accession Number : AD0117999


Title :   A SIMPLE PROOF AND SOME EXTENSIONS OF THE SAMPLING THEOREM


Corporate Author : STANFORD UNIV CA


Personal Author(s) : PARZEN, EMANUEL


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/117999.pdf


Report Date : 22 Dec 1956


Pagination or Media Count : 19


Abstract : The sampling theorem states essentially that if the frequency spectrum, or Fourier transform, g(w) of a time function f(t) vanishes for w outside some interval I , then f(t) is completely determined by its values at certain discrete sampling points, whose density is proportional to the length of the interval I . This note gives a method of proof of the sampling theorem, both for the case where the interval I is centered at the origin and where it is not, which is somewhat simpler than the previously given proofs, and at the same time is more rigorous, and yields several useful generalizations to functions of several variables and random functions.


Descriptors :   *SAMPLING , *FOURIER ANALYSIS , SPECTRA , DISCRETE DISTRIBUTION , STATISTICAL ANALYSIS , THEOREMS


Subject Categories : Statistics and Probability


Distribution Statement : APPROVED FOR PUBLIC RELEASE