REPRESENTATION AND ANALYSIS OF SIGNALS. PART XXV. PROPERTIES OF NON-GAUSSIAN, CONTINUOUS PARAMETER, RANDOM PROCESSES AS USED IN DETECTION THEORY.
JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF ELECTRICAL ENGINEERING
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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 Nxt, 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.