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THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



FREQUENCY 

 (a) FREQUENCY CHARACTERISTIC 



r, = 77/Ws = — ^ TIME >■ 



(b) IMPULSE CHARACTERISTIC 



Fig. 12 — Sjmimetrical band-pass characteristic with gradual cut-off and 

 associated impulse characteristic. In-phase and quadrature components shown 

 with respect to cor = wm — w» • 



characteristic is shown in Fig. 13. The supplementary amplitude charac- 

 teristic and the impulse characteristic are obtained by making co^ = wi 

 in (4.05) and 4.07). 



The resultant amplitude characteristic between co = and co = 2coi 

 in this case becomes 



A(a;) = 



1 



1 + COS 



ZO)] 



= COS 



2 TTCO 



4coi' 



and the impulse characteristic: 



fwi sin 2coi/o 



P(0 = 



(5.01) 



(5.02) 



TT 2coi^o[l — (2coiio/7r)-] ' 

 where coi is the bandwidth to the half -amplitude point on the trans- 



