Central Limit Theorem in the Functional Approach

摘要: The central limit theorem is proved within the framework of functional approach for signal analysis. In this framework, a modeled as single function time rather than stochastic process. Distribution function, expectation, and all familiar probabilistic parameters are built starting from by resorting to concept relative measure. Furthermore, independence among functions can be introduced. paper it shown that if sequence independent signals fulfills some mild regularity assumptions, then asymptotic distribution appropriately scaled average such has limiting normal distribution. useful when only one realization available no ensemble realizations observed or exists. obtained results also allow rigorously justify models channels up now have been derived deterministic description phenomena which inferred model invoking not ergodicity property. An application statistical characterization output multipath Doppler channel presented.