ORFANIDIS, CHAPTER 3, PROBLEM 3.8

Given the narrowband envelope F(z, t) of a propagating pulse as in Eq. (3.5.5), show that it satisfies the identity: ej(kk0)z F(0, 0)=

F(z, t)ej(0)t dt Define the "centroid" time t(z) by the equation t(z)= ' ' t F(z, t) dt F(z, t) dt Using the above identity, show that t(z) satisfies the equation: t(z)= t(0)+k 0z (3.12.2) Therefore, t(z) may be thought of as a sort of group delay. Note that no approximations are needed to obtain Eq. (3.12.2).