Filtering Non-Stationary Signals
N. A. Abdrabbo, Mark Priestley · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1969
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 analogue of the Wiener–Kolmogorov treatment of the stationary case, and show that the optimum filter is uniquely determined by the form of the evolutionary spectra.