592 BELL SYSTEM TECHNICAL JOURNAL 



(A -}- B — C)-type products, for example, are also normally dis- 

 tributed in product volume with average value 24 db less than the 

 product produced by three 0-vu talkers and standard deviation 6^13 

 or 10.4 db. To obtain the product volume corresponding to the 

 average power of the product distribution, .115(10.4)2 or 12.4 db must 

 be added. In general if Vop of an x-type product is desired, it may be 

 expressed as rjxVo + .llSXicr^ where rix is the order of the jc-type 

 product, and the value of X^ is given by the square of the coefficient 

 of a in the third column of Table !.■* We observe that VxVo + .llSXxO-^ 

 = VzVop + .115(Xx — r?x)o'^, and that \x = Vx for x = A ± B and 

 A ±B ±C. 



The frequencies present in a typical commercial speech channel 

 extend over a range of approximately 3000 cycles. The spacing of 

 carrier frequencies must be made somewhat greater than this to allow 

 for filter cut-offs. Figures 1 and 2 illustrate the spectra of the various 

 second and third order modulation products resulting from two and 

 three fundamental channel spectra respectively which are flat from 

 10 per cent to 80 per cent of the carrier spacing. Actual speech 

 channels would have peaked spectra but the results would be roughly 

 similar. Each second order band of products occupies twice the fre- 

 quency range of one original speech band, and a third order band of 

 products spreads over three times the fundamental range. Portions 

 of one product band may thus be received in different channels, but 

 with one part usually much larger than the others. It is to be noted 

 that a 2^-type product band does not consist merely of the second 

 harmonics of all tones in the band A, but includes all possible sums of 

 the tones in the fundamental band. The spectrum of the 2^-type 

 product is similar in shape to that of an (A -f .B)-type product but has 

 half as much total power because only half as many sum products can 

 be formed from a single band as from two equal bands. The interfering 

 effect of a 2.4-type product from a speech channel may of course be 

 quite different in character from that of an (A + 5) -type product since 

 in the latter case the result depends on two independent talkers. 



4. The Noise Resulting from Modulation Products 



It will be noted that the interference produced as described above 

 may be classified as unintelligible, since in products involving one 

 channel, the wave form is distorted, and in products involving more 

 than one channel, sums and differences of independent signal frequen- 

 cies are heard. It may be said therefore that interchannel modulation 



* In general for a (niiA it Wj-B ± ntsC ± • • O-product, Xj^ = Wi^ + «^2^ + ^3^ 

 + ■■■. 



