■34 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



is always the same, for a sequence of pulses the resultant envelope of the 

 recei\'ed pulse train will depend on the in-phase and quadrature com- 

 ponents.^ The reason for this is that one has even and the other odd 

 symmetry about the peak amplitude of the envelope for a single pulse, 

 when the phase characteristic is linear. 



In order to compare the transmission performance as the reference or 

 carrier frequency is changed, it is necessary to determine the in-phase 

 and quadrature components for each carrier frec^uency under considera- 



A 



J-, 



^. 



FREQUENCY, a; 



Fig. 6 — Decomposition of amplitude characteristic CEi asymmetrical with 

 respect to wr into a component di of even symmetrj' and a component (Js of odd 

 symmetry about wr . When the phase shift is linear, (Ji = d-i + Cls . 



tion. One method is to evaluate integrals (2.10) and (2.11) for each 

 Carrie frequency, which may be facilitated by resolving the transmis- 

 sion-frequency characteristic into symmetrical and anti-symmetrical 

 components as indicated in Fig. 6. This, however, is a rather elaborate 

 procedure which can be avoided with the aid of a simple translation 

 from one reference or carrier frec^uency to another, as shown below, 

 provided the in-phase and quadrature components or the envelope has 

 been determined for one reference frequency. 



Equation (2.09) may also be written, with tp = (p(t): 



P{t) = cos(co./ - ^r - <p) Pit), 



= COS{cOrt — \l/r) COS (p P{t) -f Sin(c0r^ — ypr) slu <p P(t). 



(2.13) 



