Spectral Analysis via Quadratic Frequency-Smoothing of Fourier-Transformed, Overlapped, Weighted Data Segments

摘要

A generalized framework for spectral analysis is presented, which includes as special cases the Blackman-Tukey technique and the weighted overlapped segment-averaging FFT technique. The general method is analyzed in terms of the mean and variance of the spectral estimate, thereby revealing the fundamental dependence of its performance on the temporal weighting, lag weighting, amount of overlap, number of pieces, available data record length, and frequency resolution. To enable a fair tradeoff study and comparison between many different special cases of the technique, it is demanded that the spectral analysis technique achieve a specified frequency resolution with the given data record length. This necessitates a detailed investigation of the windowing capabilities of the temporal and lag weightings, their interaction, and the definition of an overall effective weighting and window. The possibility of using lag-reshaping to achieve desirable effective windows is considered and found to be reasonable for a wide variety of windows with good side lobe behavior and decay rates. Results for the variance of the spectral estimate for rectangular temporal weighting indicate that if the length of the temporal weighting is selected to be somewhat larger than the length of the lag weighting, the variance is at a near minimum.