CARRIER AND SIDE-BANDS IN RADIO TRANSMISSION 111 



apparent pitch of the sound is half way between the frequencies of 

 the two equal components, and so the normal voice frequency will be 

 heard. With large frequency displacements of the carrier the two 

 displaced speech waves, being of equal intensity, will be more easily 

 distinguished than in the case of the single side-band. 



It is interesting to note that this result, as well as the frequency 

 shift that occurs with a single side-band, follows directly from the 

 relations arrived at above for the phase displacement of a synchronous 

 carrier. The non-synchronous carrier may be thought of as a syn- 

 chronous one the phase of which is varied with the frequency of the 

 departure from synchronism. With a single side-band it was shown 

 that a phase displacement of the carrier affects only the phase of the 

 reproduced component and that it changes this by an amount equal 

 to its own displacement. This progressive phase displacement in 

 all the components of the reproduced wave is, of course, equivalent 

 to a change in their frequencies equal to the frequency displacement 

 of the carrier. With both side-bands present, a phase displacement 

 was shown to have no effect on the phases but to change the ampli- 

 tudes of the reproduced components by the factor cos rj. Thus a 

 progressive change in r\ will cause a cyclic variation in amplitude 

 having two minima for each cycle of 77; that is, a frequency of 2w. 



If the two side-bands are accompanied by the carrier there are 

 added the beat note of the two carriers and the components of the 

 original signal. The addition of a small amount of this speech of 

 uniform amplitude to that of varying amplitude already present 

 merely tends to make the variation slightly less pronounced. From 

 the foregoing it appears that for telephony the most favorable condi- 

 tion for using a local carrier which is out of synchronism is that in 

 which only one side-band is transmitted. Fairly considerable fre- 

 quency variations are then permissible and asynchronous operation 

 appears to have practical possibilities. 



For telegraphy the case is quite different. In the first place the 

 important components of telegraph signals are much lower in fre- 

 quency, so that the side-band lies closer to the carrier, and a much 

 smaller absolute displacement of the carrier frequency is needed to 

 give the same effect as in the telephone case. Considering only such 

 small displacements, it appears that the general addition or sub- 

 traction of frequencies which occurs with a single side-band will alter 

 the shape of the signals quite seriously. The slow fluctuations in 

 signal intensity which occur with both side-bands are probably less 

 serious over most of the cycle. However, they might well cause some 

 signals to be lost entirely each time the intensity passed thru zero. 



