THEORETICAL FUNDAMENTALS OF PT'LSE TR ANSAIISRION 



and delay distortion 



d^(u)/du = 2^u,d<lf{-n)/du = -2/3u. 



(11.02) 



(The symbol (3, together with a, r/, a and J> used later in this section do 

 not have the same meaning as in earlier sections.) With (11.01) in (2.10) 

 and (2.11), the in-phase and quadrature components in (2.09) become 



9/^ r°° 



/?_ + -R+ = — / Q:(w.) cos ut cos /3?(^, and 

 T Jo 



9^ r" 

 Q_ + Q4. = — / (i(u) cos ut sin i3n^. 

 TT Jo 



(11.03) 



The in-phase and quadrature components can accordingly be identi- 

 fied with the real and the negati^'e imaginary component of the integral 



9^ r"^ 

 J=— a{u) cos ute''^"\hi. (11.04) 



X Jo 



The solution of this integral is rather simple for the particular case of a 



Gaussian transmission characteristic 



a (m) = e' 



in which case 



J = - I e 



IT Jo 



-{a + i^)ii^ 



COS ut du, 



(11.05) 



(11.06) 



-t^H{a+i0) 



[T{a+mY'-' 



AMPLITUDE CHARACTERISTIC 



/PHASE CHARACTERISTIC, /}U2 

 DELAY DISTORTION, 2/3U 



FREQUENCY 



-2/3u 



Fig. 40 — Symmetrical band-pass amplitude characteristic with linear delay 

 distortion. 



