Dimensionality of Crosstalk Functions

Abstract

We study the dimensionality for the class of near-end crosstalk functions in a cable. The dimensionality is closely related to the distribution of eigenvalues for a particular integral operator that we call the energy operator. We find bounds for these eigenvalues in terms of the eigenvalues associated with the prolate spheroidal waveforms studied by Landau, Pollak, and Slepian. The important technical observation, permitting us to use their results, is that though the crosstalk functions are not band-limited, the degree to which they are band-concentrated can be uniformly specified.