Accession Number : AD0434120


Title :   SOME OBSERVATIONS ON MEASURABLE PROPERTIES OF RANDOM PROCESSES AND FIELDS. I,


Corporate Author : LITTON SYSTEMS INC WALTHAM MASS


Personal Author(s) : Middleton,David


Report Date : 16 Mar 1964


Pagination or Media Count : 54


Abstract : A number of useful, measurable properties of random processes and random fields are de,ined and discussed, and it is shown how these results may be applied to observations necessarily finite in time and in space. Time and space stationarity and ergodicity are considered, as are the definition and construction of hierarchies of probability distribution (densities) defining these stochastic processes and fields. The notion of the intensity spectrum in one or more dimensions is introduced, along with extended versions of the Wiener-Khintchine theorem relating the spectrum to the covariance functions. Cross- and auto-spectral densities are also briefly treated. Some tests of practical stationarity and homogeneity are suggested for finite data sets and single representations, from which approximately statistical (or regular) properties of the ensemble as a whole may be deduced. (Author)


Descriptors :   MATHEMATICAL PREDICTION , PROBABILITY , STATISTICAL FUNCTIONS , STATISTICAL PROCESSES , STATISTICAL TESTS , UNDERWATER , MEASUREMENT , SAMPLING , INFORMATION THEORY , SERIES(MATHEMATICS)


Distribution Statement : APPROVED FOR PUBLIC RELEASE