THEORETICAL FUNDAMENTALS OF PULSE TRANSMISSION I .)0 



For amplitudes h > 1, it is necessary to consider a greater number of 

 echoes, as "will be evident from Table I for b = 1, 2, 5, 10 and 15 radians. 



The preceding equations apply to low-pass characteristics and also 

 to sj-mmetrical bandpass characteristics, as shown in Fig. 19. In the 

 latter case a(ii) = a(-u) and ^(-ii) = -^(u) in (2.10) and (2.11) 

 so that R+ = R- and Q+ = Q- and (2.09) becomes 



P{t) = cos (c^rt - ypr) R{t), 



(6.07) 



where R(t) = R+ + R- and co, = w,„ = midband frequency. The en- 

 velope R(t) is accordingly obtained by replacing Po(t) in (6.05) by Ro(t), 

 the envelope in the absence of phase distortion. 



In Fig. 21 is shown a particular case of a sine deviation in the phase 

 characteristic and the corresponding delay distortion, which approxi- 

 mates that encountered in many instances. For a low-pass system the 

 phase and delay distortion would be as shown for u > 0. In this particu- 



Jdi. 



AMPLITUDES OF PULSE ECHOES 



±k. 



(a) 



-Ji 



Po(t+2r) Po(t+r) 



Po(t) 



Po(t-r) Po(t-27-) 



J2Po(t+2r 



;— RESULTANT PULSE P(t) 



.JoPo(t) 



J2(Po-27-) 



(c) 



(d) 



Fig. 20 — Determination of resultant pulse by superposition of pulse echoes. 



