Multivariate Multiple-Window Spectrum Estimates

We describe the estimation of coherence, cross-spectra, transfer functions, and related multivariate time-series entitles using the multiple- window approach. This method of spectrum estimation (Proc. IEEE 70, pp. 1055-96, 1982) differs from conventional approaches in that an orthogonal set of data tapers is applied to the data before transforming. The tapers, or data windows, are discrete prolate spheroidal sequences characterized as being the most nearly bandlimited functions possible among functions defined on a finite time domain and so have very low "leakage." The method is essentially a small-sample inverse method applied to the finite Fourier transform.