. The Bell System technical journal . tic of bandwidth wi — coo = 2cos if coo is a multiple of oji — wo . It shouldbe noted however, that this pulse transmission rate cannot actually berealized since the phase characteristic will have infinite slope, so thatthe transmission delay will be infinite. In addition, the zero frequencyphase intercept xpo must be ztmr, a condition which cannot be attainedor remain stable in view of the infinite slope of the phase characteristic. With the envelope given by the factor sin UsU/wsh in (), thein-phase and quadrature components for any reference frequen
. The Bell System technical journal . tic of bandwidth wi — coo = 2cos if coo is a multiple of oji — wo . It shouldbe noted however, that this pulse transmission rate cannot actually berealized since the phase characteristic will have infinite slope, so thatthe transmission delay will be infinite. In addition, the zero frequencyphase intercept xpo must be ztmr, a condition which cannot be attainedor remain stable in view of the infinite slope of the phase characteristic. With the envelope given by the factor sin UsU/wsh in (), thein-phase and quadrature components for any reference frequency canbe determined with the aid of (). If the lower band-edge is selected, o)t = coti, then w,j = oj,. With a linear phase characteristic \py = wTd ,so that in () Wyt — ^y = o^sk ■ The in-phase and quadrature com-ponents are accordingly obtained by multiplying the envelope by cosWsU and sin , respectively. As an alternate method, the two components can be obtained from AMPLITUDE VS FREQUENCYCHARACTERISTIC. Fig. 9 — Special case of idealized band-pass characteristic in which wi = 2woand resultant impulse characteristic is zero at intervals 7-0=;^. 740 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 (), which with i?_ = 0, Q_ = 0 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 () () () where cob = 2us is the bandwidth. It wilJ be noticed that R+ and Q+ areobtained by multiplying the envelope by cos UsU and sin co^^o in accord-ance with (). (a) FREQUENCY CHARACTERISTICS (b) IMPULSE CHARACTERISTICS
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