594 BELL SYSTEM TECHNICAL JOURNAL 



5. Relation Between Speech and Sine Wave Modulation 



A goal of our investigations is to express the requirements finally in 

 terms of measurements which can be made on amplifiers with sinu- 

 soidal testing waves. A means of relating modulation products pro- 

 duced by speech channels to those occurring when discrete frequencies 

 are applied is therefore needed. For our purposes here we shall 

 express the needed relation ^ in terms of a "Speech-Tone Modulation 

 Factor," which we shall abbreviate as S.T.M.F. and define in terms 

 of the following procedure: Apply the fundamental single-frequency 

 test currents necessary to produce the product in question, which we 

 shall designate as an x-type product. Adjust each fundamental to 

 give mean power of one mw. at the zero level point of the system. 

 Measure the resulting x-type product at the point of zero transmission 

 level of the system. Suppose the product is Hx db below one funda- 

 mental. Next load the system with speech from the combination of 

 fundamental talkers required to form the talker product of x-type. 

 Each talker must produce speech volume of vu at the transmitting 

 toll switchboard or point of zero transmission level. The product is 

 then received from the appropriate channel and a comparison is made 

 between it and the speech from one talker with both talker and product 

 at the same transmission level point in the system. The comparison 

 should be made on the basis of relative interfering effect. Suppose it is 

 determined that an x-type product is Lx db below one 0-vu talker. 

 Then Sx, the S.T.M.F. for an x-type product, is defined by 



Sx = Lx- Hx. (5.1) 



The sign of the S.T.M.F. has been assigned here to be positive when 

 the difference in db between effect of talker and talker product is 

 greater than the difference between sine wave fundamental power and 

 sine wave product power. 



It is to be noted that not only does each type or product possess 

 its own S.T.M.F., but also that the several portions of a product ap- 

 pearing in different channels have different S.T.M.F.'s. This may 

 be clearly seen from Figs. 1 and 2. We note also that the S.T.M.F. 

 is a property of the system on which the measurements are made, since 

 it varies with the band width of the channels, the spacing of carrier 

 frequencies, and the extent of departures from the simple square and 

 cube law representation of the amplifier characteristic. It also varies 

 with the type of transmitting and receiving instruments used. Theo- 



*The quantity here defined is related to what has been called "staggering advan- 

 tage" of modulation products. Since the term "staggering advantage" has been 

 applied to various kinds of interference including linear crosstalk, its use here might 

 lead to confusion and is avoided. 



