THEORETICAL FUNDAMENTALS OF PULSE TRANSMISSION 991 



ference and thus the maximum transmission capacity or optimum per- 

 formance in other respects for a given bandwidth. In the following sec- 

 tions this problem is discussed further. 



13. TRANSMISSION LIMITATIONS IN SYMMETRICAL SYSTEMS 



In a symmetrical system the amplitude characteristic has even sym- 

 metry and the phase characteristic odd symmetry with respect to a 

 properl}^ chosen frequency. A low-pass transmission system is thus 

 symmetrical with respect to zero frequency, when the negative fre- 

 (juency range is included. A double sideband system is symmetrical if 

 the amplitude characteristic has e\-en and the phase characteristic odd 

 symmetry with respect to the mid-band frequenc3^ 



Equation (12.06) applying to a low-pass system or baseband trans- 

 mission may be written 



00 



W{0) = AoP(O) + E [AnPM -f A.nPi-nr)]. (13.01) 



Let it be assumed that pulses of varying but discrete amplitudes are 

 transmitted, with a maximum peak amplitude equal to /Lmax and a 

 minimum peak amplitude Amin . If q pulse amplitudes are employed, 

 the difference between peak amplitudes is then (/Imax ~ Amin)/(q — 1). 

 Let P^ designate positive values of P{nT) and P~ the absolute value of 

 negative amplitudes. 



The maximum value of W{Qi) when a pulse of amplitude Ao is trans- 

 mitted at the sampling point n = is then 



CO 



TF„.ax = ^oP(O) -\- E A^J^P-^M + P'^i-nr)] 



n=l , . 



(13.02) 

 - Z ^mi„[P"(nr) + p-i-nr)] 



n=l 



The minimum amplitude of W(0) when a pulse of the next higher am- 

 plitude ^0 + (-4 max — Amin)/(? — 1) IS transmitted becomes 



TFmin = ( Ao + ^^^ ^^^ ) P(0) 



[P'inr) + P'i-nr)] (13.03) 



+ E Ami. [P-'(nr) + P''(-nr)]. 

 To permit distinction between the two pulse peaks it is necessary that 



