
Accession Number : AD0640866
Title : A GENERAL SAMPLING THEOREM.
Descriptive Note : Technical rept.,
Corporate Author : CRUFT LAB HARVARD UNIV CAMBRIDGE MASS
Personal Author(s) : BUDELIS,J. ; Abramson,N.
Report Date : JUN 1966
Pagination or Media Count : 18
Abstract : The usual form of the sampling theorem states that a function a(t), whose Fourier Transform A(f) vanishes outside the interval (w, w) may be reconstructed exactly from its values at equally spaced sampling points taken at the 'Nyquist Rate' of 2w points per second. It is also known that a(t) may be reconstructed from its sample values taken at half the Nyquist rate if in addition we use the same number of samples from certain functions derived from a(t) (e.g., its Hilbert Transform or its derivative). In this paper the authors derive necessary and sufficient conditions in order that a(t) may be reconstructed from sample values of rather general functions b sub 1 (t), b sub 2 (t). . . b sub n (t) where the values of each b sub i (t) are taken at 1/n times the Nyquist rate. In addition, the sampling functions necessary for reconstruction are exhibited directly as the solutions of a linear matrix equation. This result includes as special cases kderivative sampling, irregular spacing sampling and Hilbert Transform sampling. (Author)
Descriptors : (*THEOREMS, *SAMPLING), INTEGRAL TRANSFORMS, BANDWIDTH, FREQUENCY, INFORMATION THEORY
Subject Categories : Numerical Mathematics
Cybernetics
Distribution Statement : APPROVED FOR PUBLIC RELEASE