14 BELL SYSTEM TECHNICAL JOURXAL 



nole ma>' be neglected is extremely small. On the other hand this 

 area increases very rapidly as the attenuation increases. 



We may use the same sets of curves in considering the displaced 

 side band interference. From Fig. 2 it is evident that by far the most 

 important components of this interference are those represented by the 

 {q ± ii) group. In order to estimate this interference we must follow 

 some rule for coml)ining the q -\- n component with the q — u com- 

 ponent. In order to do this in a strictly correct manner we should 

 have to take into account the frequencies and sensation levels of the 

 components. However, it has been shown ' that over a considerable 

 portion of the audio frequency range, and for sensation levels of 

 approximateh' the magnitude in which we are interested, the inter- 

 fering effect of these frequencies may be taken to be approximately 

 equal to that due to a single frequency of twice the amplitude of 

 either component. We shall therefore take our data from the dash-dot 

 curve of Fig. 2. h'rom this curve it appears that if the displaced side 

 band interference is to be 40 db down from the desired speech, we must 

 have a carrier ratio of 0.002, while if it is to be 20 db down from the 

 desired speech the corresponding carrier ratio is 0.02. The curves 

 corresponding to these values are shown by 2 and 6, respectively, on 

 Figs. 5 and 6. 



From this it appears that the area in which the side band noise is not 

 objectionable may be a great deal larger than that in which the carrier 

 beat is of a tolerable intensity. If the frequency of the carrier beat is 

 reduced below the useful audible range then the former area may be 

 considered to be entirely free from interference of any kind. Conse- 

 quently, it is highly desirable to limit the maximum possible differences 

 in the carrier frequencies to a value which is definitely below the audio 

 frequency pass band of commercial radio receivers and loud speakers. 



Turning now to the undesired speech, we note that it is of very little 

 importance compared with the displaced side band interference. Thus, 

 if this speech is to be 40 db down from the desired speech, the value of 

 the carrier ratio is 0.044 for the case of a square law detector, while for a 

 difference in level of 20 db, the carrier ratio is 0.14. A curve for the 

 case of a 40 db difference is indicated by 7 of F"ig. 5. 



The comparison between curves 7 and 6 emphasizes the fact that we 

 may have considerable areas of intolerable displaced side band inter- 

 ference in which the intelligible speech from the undesired station is 

 not noticeable. Of course, this interference is often classed as distorted 

 speech but the distinction is convenient in the present discussion. 



^ J. C. Steinberg, "The Relation Between the Loudness of a Sound and its Physical 

 Stimulus," Phys. Rev., Sec. Ser., Vol. 26, pp. 507-523. 



