Multi-window Bispectrum Estimates

In many applications where the use of higher-order spectra is desirable, use of conventional methods is hampered by lack of data or, equivalently, by the evolutionary nature of the process. Here we describe a multiplewindow method for computing consistent estimates of the bispectrum from a short segment of the process. In multiple-window methods the information in a narrow band is summarized by the coefficients of its expansion in Slepian sequences (discrete prolate spheroidal sequences). Bispectrum estimates are then formed either by averaging what are effectively complex demodulates over time, or by averaging products of such expansions centered at frequencies f 1, fz, and - f 1 - fz over a three-dimensional element of the frequency domain. Either choice reduces to a weighted average of products of the expansion coefficients.