600 BELL SYSTEM TECHNICAL JOURNAL 



If we assume that the total modulation noise allowable for an x-type 

 product is X db above reference noise at zero level, we may equate X 

 to Wx in (7.6) and solve for Hx, giving 



Hx= F, + r„ - 5, - X. (7.7) 



Substituting the value of Vx from (7.4) in (7.7), we get for the system 

 requirement in terms of allowable ratio of fundamental to product 

 when there is one mw. of each fundamental at the point of zero trans- 

 mission level: 



Hx = Ta-\- VxVop — Sx -{- .115(Xx — Vx)o^ 



+ 10 logio vxk + lOju(x) logio T — pxv — X. (7.8) 



For the convenience of the reader, the following recapitulation of 

 significance of the symbols used in (7.8) is given: 



Hx = Ratio in db of power of each single frequency fundamental 

 to power of resulting 3c-type product when each fundamental 

 has power of one mw. at point of zero transmission level. 

 Ta = Reading of 0-vu talker on noise meter in db above reference 



noise. 

 77^ = Order of x-type product. 

 Vop = Volume in vu corresponding to the average power of the talker 

 volume distribution at the point of zero transmission level 

 = Fo + .1150-2 where Va is average talker volume in vu. 

 0" = standard deviation in db of talker volume distribution. 

 5x = Speech-Tone Modulation Factor of x-type product as defined 



in Section 5. 

 X^ = Vwi^ + W2^ + • • • for (miA ± mzB ± • • ^-type product. 

 Vxh = total number of x-type products which can fall in channel with 

 carrier frequency kp. See Table II. 

 ju(x) = number of distinct fundamentals required to produce x-type 

 product. 

 T = fraction of busiest hour that a channel is active. 

 Px, = correction to be applied to S.T.M.F. when p products are 



superimposed. Defined in (7.1)-(7.3). 

 X = Allowable modulation noise in channel in db above reference 

 noise at zero transmission level point. 



The allowable noise may be divided equally between second and 

 third order purely on a power basis by setting the requirement for 

 each 3 db more severe than the total value allowed, or it may turn out 

 that the noise from one order is much more difficult to reduce than 

 that of the other in which the full allowance may be given to the more 



