Spectral estimation using combined time and lag weighting

This paper presents a five-step method for spectral estimation that combines time and lag weighting and leads to a procedure that requires less than one-half the computations of standard methods. The Blackman-Tukey method and the Weighted Overlapped Segment Averaging (WOSA) method (widely used in sonar and other applications) are shown to be special cases of the combined method. An analysis of the mean value of the spectral estimate leads to an unusual lag weighting that corrects for poor (for example, rectangular) time weighting and affords effective windows with very good sidelobe behavior. Several examples of achievable windows are provided. Finally, the variance of the spectral estimate of the combined method is presented and evaluated for the case of rectangular time weighting, no segment overlap, and lag reshaping. It is found that the variance is virtually as low as any technique that realizes the same frequency resolution with the same finite data record length. Furthermore, the computational costs are less than one-half those of the WOSA method, primarily because no time weighting multiplications or overlap are required.