740 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



(2.09), which with i?_ = 0, Q_ = becomes: 



P(t) = cos wotoR+{t) + sin o:otoQ+(t), 



with 



5 r"* 



R+ = - I cos uto du, 



T Jo 



IcOb Sm Wh/() 2fcOs , sill COs/o 



■ = COS Wglo 



Q+ = - I sill i</o <ii<, 

 TT Jo 



and 



Sub 1 -~ COS (jjbto 25cos • J sin cogfo 

 ^ = sm usto — , 



TT COfefo TT OJslO 



(3.06) 



(3.07) 



(3.08) 



where cob = 2us is the bandwidth. It wilJ be noticed that R+ and Q+ are 

 obtained by multiplying the envelope by cos UsU and sin co^^o in accord- 

 ance with (2.19). 



(a) 



FREQUENCY CHARACTERISTICS 



(b) 



IMPULSE CHARACTERISTICS 



.J, 



Fig. 10 — Idealized transmission characteristic with gradual cut-off, 3, ob- 

 tained by superposition of characteristic with sharp cut-off, 1, and characteristic, 

 2, with odd symmetry about coj . Linear phase shift assumed. 



