A SIMPLE PROOF AND SOME EXTENSIONS OF THE SAMPLING THEOREM
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 22, 1956
- Accession Number
- AD0117999
Entities
People
- Emanuel Parzen
Organizations
- Stanford University