Accession Number : AD0675811

Title :   THE DIGITAL FORM OF OPERATORS ON BAND-LIMITED FUNCTIONS,

Corporate Author : GENERAL ELECTRIC CO SANTA BARBARA CALIF TEMPO

Personal Author(s) : Kramer,Henry P.

Report Date : DEC 1967

Pagination or Media Count : 21

Abstract : Functions whose spectrum is limited to frequencies symmetrically situated with respect to zero and contained either in one interval (low-pass) or in two intervals (band-pass) can be represented faithfully by their values at equidistant points in time. If such functions are represented by a table of numbers in a computer, it is important to know by which operations on these numbers various operations of analysis are represented. The present report gives in detail the representation of differentiation, convolution, Fourier transformation and Hilbert transformation. It is shown how the latter operation is used to obtain the amplitude and phase of the band-limited function from the sampled data. The justification of the formulas is based on the theorem that every bounded operation on B, the space of band-limited functions, can be applied term by term to the Whittacker-Shannon representation of a band-limited function. (Author)

Descriptors :   (*SIGNALS, PROCESSING), (*INFORMATION THEORY, *FUNCTIONAL ANALYSIS), OPERATORS(MATHEMATICS), INTERPOLATION, SAMPLING, BANDWIDTH, INTEGRAL TRANSFORMS, THEOREMS, DIGITAL COMPUTERS, HILBERT SPACE, FOURIER ANALYSIS, NUMERICAL METHODS AND PROCEDURES

Subject Categories : Theoretical Mathematics
      Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE