Spectrum Management in Telephone Loop Cables, II: Signal Constraints That Depend on Shape

Instantaneous near-end crosstalk interference depends only on the shape of the signals transmitted on the disturbing pairs during an interval of duration determined by cable properties that immediately precedes observation of the interference. It is shown that these shapes can be resolved into a linear combination of a finite number of orthonormal functions that cause significant crosstalk and a function that does not cause substantial crosstalk. The orthonormal functions are the solution of an equation that depends on the statistical properties of the crosstalk.