Optimum Window Length for the Measurement of Time‐Varying Power Spectra

In analyzing a nonstationary time series, one often encounters the problem of estimating associated time‐varying autocorrelation functions and power spectra. This paper proposes a method of estimating the time‐varying autocorrelation functions and power spectra whereby the nonstationary time series is first divided into a number of windows. The time‐invariant autocorrelation function and power spectrum for each window are then determined under the ergodicity assumption. The most important step in this procedure—namely, selection of an optimum window length—is based on the equation derived by Berndt and Cooper [IEEE Trans. Inform. Theory IT‐11, 307–310 (1965)]. Implementation of the equation for the purpose of establishing an optimum window length is described. A numerical example for the measurement of time‐varying power spectrum is given to illustrate its application. The result of this example indicates that the optimum window length thus established coincides with the intuitively “best” window length.