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THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



A(ajr+u) = t¥(u) 



PHASE 



AMPLITUDE 



A(a;r--u) = 



Fig. 5 — Transfer of reference frequencj'^ from co = to co = cor . 



pulses or that otherwise the above modification is applied, in which 



case 



P(0 = - [ A(w) cos M - '/'(w)] d<^. (2.07) 



In the latter equation A(co) can also be regarded as the frequency 

 spectrum of a pulse applied to a transmission system having a constant 

 amplitude characteristic and a phase characteristic i/'(co) over the band 

 of the pulse spectum. 



Equation (2.07) applies to any type of transmission-frequency char- 

 acteristic and is convenient in this form for low-pass characteristics. For 

 band-pass characteristics as shoA\ai in Fig. 5 however, it is convenient 

 from the standpoint of general analysis as well as for numerical evalua- 

 tion to use a reference frequency cor within the tranmsission band, that 

 is, to employ the transformation 00 = 0;^+ » db^ = du. 



With the notation 



a(w) = yl(co) = A{U + COr), 



^(lO = i/'(w) - i/'(w,) = 1^(0;) - l/'r, 



(2.08) 



