Estimation of Time-Varying Correlation Functions

The need for estimating the auto- or crosscorrelation functions of nonstationary random processes frequently arises in communication and self-adaptive systems. In most situations only one sample function can he observed over finite time. It is the purpose of this work to establish a firm theoretical basis for such a measurement of time-varying correlation functions, and the emphasis here is on suitable estimation procedures rather than specific measurement techniques. Second order stochastic processes are used as a mathematical model. The minimum mean square error between a weighted time average and the true (ensemble average) correlation function is investigated. This procedure leads to an optimum weighting function which can be obtained numerically under the Gaussian assumption. The results of such an analysis justify the much simpler finite integration-time average as an estimate. By employing a bilinear approximation in time t and delay t to the true correlation function, the mean value and variance of the simple finite-time average are found. A minimum upper bound on the mean square error is used as a criterion for an optimum observation time of such an estimate. Explicit results, however, require again the Gaussian assumption. These approaches are based mainly on a strict error analysis. A more direct approach, that leads to approximants which are random variables with unknown properties, is also outlined. The restrictions and difficulties are discussed. Examples to support the proposed estimation procedures are presented and explicit results appear mostly in graphical form

Cerebral regional tissue Oxygen Saturation to Guide Oxygen Delivery in preterm neonates during immediate transition after birth (COSGOD III): an investigator-initiated, randomized, multi-center, multi-national, clinical trial on additional cerebral tissue oxygen saturation monitoring combined with defined treatment guidelines versus standard monitoring and treatment as usual in premature infants during immediate transition: study protocol for a randomized controlled trial

Background: Transition immediately after birth is a complex physiological process. The neonate has to establish sufficient ventilation to ensure significant changes from intra-uterine to extra-uterine circulation. If hypoxia or bradycardia or both occur, as commonly happens during immediate transition in preterm neonates, cerebral hypoxia–ischemia may cause perinatal brain injury. The primary objective of the COSGOD phase III trial is to investigate whether it is possible to increase survival without cerebral injury in preterm neonates of less than 32 weeks o

ESTIMATION OF TIME-VARYING CORRELATION FUNCTIONS.

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