Efficient Thomson Spectral Estimator with Time-shifted Windows

In this paper optimal spectral analysis window shapes, using weighted discrete prolate spheroidal sequences as basis functions, are proposed. These windows are not typically positive or even. The windows are time-shifted, combining the computational efficiency of the Welch method and the appealing property of predefined frequency resolution of the Thomson spectral estimator. The parameters of the optimal windows are found by minimising the resulting spectral covariances and optimising the window overlap, for the predetermined frequency resolution and number of windows. The windows are found to have low side lobes, giving small spectral leakage, and the final spectral estimate gives close to optimal variance reduction, i.e. the covariance between different sub-spectra is very small.