REPRESENTATION AND ANALYSIS OF SIGNALS. PART XXV. PROPERTIES OF NON-GAUSSIAN, CONTINUOUS PARAMETER, RANDOM PROCESSES AS USED IN DETECTION THEORY.
Abstract
The conclusions of the report are: (1) The expansion coefficients of some common representations of random processes will be independent only when the process is Gaussian; (2) Processes representable on a particular interval in terms of a denumerable sequence of independent random variables will often have sample function properties similar to those of the Gaussian process; (3) The quadratic variation of non-Gaussian processes with sufficiently smooth cumulants is constant for a given interval; (4) The quadratic variation of a non-Gaussian linear process equals the sum of the squares of its jump discontinuities; (5) There is a class of sequences of functionals, say T sub N(x(t)), such that l.i.m. T sub N equals the quadratic variation of the processes in (3). (6) The necessary and sufficient condition for singular detection of a sure signal in Gaussian noise is sufficient for singularity when the noise is any mean square continuous process. (7) Regularity or singularity for signals depending on a random parameter, gamma, is implied by regularity or singularity for signals corresponding to each possible value of gamma when gamma has a discrete distribution or the noise is Gaussian. (8) Singular estimation of certain parameters is sometimes possible under the conditions of singular detections. (9) Some of the spectral conditions which imply singularity for Gaussian random processes continue to imply singularity for non-Gaussian processes with sufficiently smooth cumulants. (10) For other non-Gaussian processes, spectral conditions are irrelevant.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1967
- Accession Number
- AD0661211
Entities
People
- Percy A. Pierre
Organizations
- Johns Hopkins University