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非平稳信号的滤波AI 解读

Summary We observe a record consisting of a “signal” plus “noise” up to the time instant t, and wish to extract the value of the signal at the time instant (t + m) by means of a linear filter. Here, m may be positive (corresponding to “prediction”) or negative (corresponding to “smoothing”). In this paper we consider the case where both the signal and noise processes are non-stationary and possess evolutionary spectral representations. Using this approach we obtain a close…

非平稳过程的预测AI 解读

Summary We consider the problem of linear least-squares prediction for a class of non-stationary processes which possess “evolutionary spectral representations”. It is shown that, under certain conditions, such processes admit moving-average representations in terms of time-dependent coefficients. This feature enables us to develop a close analogue of the Wiener–Kolmogorov approach to the corresponding problem for stationary processes.