相互相関による非定常ランダム信号の検出理論についての一考察

概要

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A method of detecting non-stationary random signals s(t) is established, which is given by cross-correlation φ_<zx>(t,t+τ) between random local inputs z(f) and received inputs x(t), where z(t) represents the output of linear time varying filters with impulse response h(t,σ): [numerical formula] and x(t) is nonlinearly coupled input, f[s(t),n(t)]. As the result, it is shown that 1) If h(t,σ) is arbitrarily given, the detection of s(t) is established based on the auto-correlation of x(t), whose simple but best model is the case in which h(t,σ) belongs to unit operator: where [numerical formula] 2) If h(t,σ) is given as the optimum filter under the least R. M. S error condition, the detection is established not directly cocerned with the property that the auto-correlation of noises vanishes in a large correlation time. 3) The detection is more effective with the use of the optimums nonlinear filters. These discussions have been made under the condition that signals and noises are not correlated.
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