(13.09) 



(13.10) 



994 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



train may be written 



00 



AT^(O) = W{0) - WoiO) = X; AnlPM - PoMl (13.08) 



n=— 00 



The rms deviation becomes, with APinr) = P{nT) — Poinr) 

 ATF(O) = a(j: [APinr)fY, 



\ n=— 00 / 



^ 4 (^ /] [^Pit)T dtj', 



= AP(0)U. (13.11) 



A is the rms ampUtude of the transmitted pulses and U the rms inter- 

 symbol interference referred to unit amplitude of the received pulses. 

 Expressions for U applying to fine structure imperfections in the trans- 

 mission frequency characteristic were given in Section 8, for a low-fre- 

 quency cut-off in Section 9 and for band-edge phase deviations in Sec- 

 tion 10. 



For balanced pulse systems employing positive and negative pulses, 

 rms intersymbol interference in the positive and negative directions will 

 be equal. For such systems the maximum value of the summation in 

 (13.02) becomes A"^(0) and in (13.03) -kWiO), where k is the peak 

 factor. Equation (13.04) is then replaced by 



M = 



— A ■ 



q- 1 



= 2Am^P{0) 



P(0) - 2kAP{0) U, 



Lq 



-i-^ - fc[/(4Mmax) 



(13.12) 



when Amin = — ^max • 



In a balanced pulse system employing q pulse amplitudes, i.e., q/2 

 positive and q/2 negative amplitudes, with equal steps 2^1 max/ (? — 1) 

 between pulse amplitudes, the following relation applies if all ampli- 

 tudes have equal probability. 



1/2 



.A/Amax — 



g+ 1 



L3(g - 1)J 



Hence, 



M = 



2Amax-P(0) 



q- 1 



1 - k 



q' - 1^^'^ 



U 



(13.13) 



(13.14) 



As mentioned before, the factor A; may be as high as 4, in which case the 



