Fundamental property of cross terms of ground transfer function

Abstract

Normalized energy density (NED) is one of the essential quantities for a ground transfer function of a 1D layered structure model. The cross term of the functions and the cross term of the power of the functions are defined as an extension of the NED. The cross term is physically defined as the correlation coefficient between the two ground transfer functions. The cross term detects the harmony of two transfer functions; a finite value is obtained only in the case where peak frequencies coincide. The cross term of the power of the normalized transfer functions is 1 when the peak frequencies do not coincide. The properties of the cross term and the cross term of the power are analytically proved for a two-layered case and numerically shown for three- and four-layered cases.