1000 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



the quadrature components may be written 



Q[±{2m - 1)t] = ±P[±(2m - 1)t], m = 1, 2, 3 



Let 



m=l 



00 



J^R~ = Z [^~(2mr) + R'{-2mr)], 



7n^ 1 



EQ"" = £ ^""[(2^ - l)r] + Qn-(2m - l)r], 



(14.04) 



EQ" = Z Q"[(2w - l)r] + Q-[ -(2m - l)r], 



where i?""", Q"*" designate positive values and R~, Q~ the absolute values 

 of negative amplitudes of the in-phase and quadrature components. 



Let it be assumed that two pulse amplitudes are employed, Am in and 

 A max • When the minimum amplitude is transmitted, the maximum value 

 of the envelope is obtained by considering the maximum positive over- 

 laps of the in-phase components in conjunction with the maximum value 

 of the quadrature component. The value thus obtained is 



Tfmax = [(^min RiO) + ^ma. Z^^)' 



It is assumed that ZQ" > ZQ^> otherwise Q~ and Q^ would be inter- 

 changed in the last term. 



When the maximum amplitude is transmitted, the minimum value of 

 the envelope is obtained by considering the maximum negative overlaps 

 of the in-phase components, in conjunction with the minimum value of 

 the quadrature component, which gives 



Wmin = [(Amax i^(0) " Amax Z^")' + ^^'min (ZQ" 



The margin for distinction between Am in and A max is M = TFmin — 

 Wma.x and becomes 



M = Amax [{R(o) - ZRy + ahq"- - ZQ-yf" 



(14.07) 



- Amax [{HR(0) + Z^^)' + (ZQ" - f^ZQyf", 



where 



