THEORETICAL Fl'XDAMENTALS OF PITLSE TRANSMISSION 



730 



tiansinittetl without mutual interference at the same rate as for a low- 

 pass charactci-istic of bandwidth wo , or at the same rate as with single 

 sidel)and transmission ovei' a baud-pass system of bandwidth con . More 

 generally, pulses can in pi'inciple be transmitted without mutual inter- 

 ference between pulse peaks at the same rate as for a low-pass character- 

 istic of bandwidth wi — coo = 2cos if coo is a multiple of oji — wo . It should 

 be noted however, that this pulse transmission rate cannot actually be 

 realized since the phase characteristic will have infinite slope, so that 

 the transmission delay will be infinite. In addition, the zero frequency 

 phase intercept xpo must be ztmr, a condition which cannot be attained 

 or remain stable in view of the infinite slope of the phase characteristic. 



With the envelope given by the factor sin UsU/wsh in (3.04), the 

 in-phase and quadrature components for any reference frequency can 

 be determined with the aid of (2.19). If the lower band-edge is selected, 

 i.e. o)t = coti , then w,j = oj,. . With a linear phase characteristic \py = wTd , 

 so that in (2.19) Wyt — ^y =" o^sk ■ The in-phase and quadrature com- 

 ponents are accordingly obtained by multiplying the envelope by cos 

 WsU and sin txi.U , respectively. 



As an alternate method, the two components can be obtained from 



AMPLITUDE VS FREQUENCY 

 CHARACTERISTIC 



Fig. 9 — Special case of idealized band-pass characteristic in which wi = 2wo 

 and resultant impulse characteristic is zero at intervals 7-0=;^. 



