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具有准线性残差的随机过程振幅谱估计札记AI 解读

It is shown that when a deterministic signal is observed in quasi-linear noise (herein defined), the usual estimate of the signal amplitude spectrum for a finite time interval converges uniformly and exponentially fast in probability to this spectrum as the length of the time interval becomes infinite. When the limiting amplitude spectrum exists, the estimate tends to this function exponentially fast but no longer uniformly, in general.

具有准线性残差的随机过程振幅谱估计札记AI 解读

It is shown that when a deterministic signal is observed in quasi-linear noise (herein defined), the usual estimate of the signal amplitude spectrum for a finite time interval converges uniformly and exponentially fast in probability to this spectrum as the length of the time interval becomes infinite. When the limiting amplitude spectrum exists, the estimate tends to this function exponentially fast but no longer uniformly, in general.