THEORETICAL FUNDAMENTALS OF PULSE TRANSMISSION 



781 



a;' OJ, FREQUENCY, OJ 



Fig. 37 — Constant amplitude characteristic with hand-edge phase distortion. 



If there is no phase distortion, i.e., /3 = 0, between co = and co', equa- 

 tion (10.03) becomes 



X = 



a'l 





COS /3 dbi 



112 I r ^Wmax- 



(10.04) 



As an example, consider a parabohc deviation from a Hnear phase 

 characteristic between w' and comax , in which case delay distortion would 

 vary linearily in this band, as indicated in Fig. 37 for a constant ampli- 

 tude characteristic for which Wmax = wi . In this case 



/3 = /3i 



COi — cu 



(10.05) 



where /3i is the maximum phase deviation, obtained for w = coi . 

 Equation (10.04) in the above case becomes: 



' \2n 



9 (•" 1 



2(coi - 



1 — cos /3i 



2(aji — a; ) 



CO 1 — CO 



Jo 



d!co, 



cos u du 



(10.06) 



COi 



1 _ 1 ( — ) (K + X) 

 2\2i3i/ 



where R -\- iX = erf {^-^'"^e"'^) in which erf is the error function. 



For a constant amplitude transmission characteristic as assumed 

 above, (r/coiTi) = 1, so that (10.02) becomes C7 = X, which may also 



