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BELL SYSTEM TECHNICAL JOURNAL 



the signal. Hence each component of the signal is represented in the 

 modulated wave by an expression of the form, 



kCScos(qt + e) cospt = \kCS {cos[{p+q)t+Q]+cos[{p-q)t-Q]\. (4) 



This represents two sinusoidal components, the frequencies of which 

 differ from that of the carrier by the frequency of the particular signal 

 component. The similar expressions for the other signal components 

 each yield a pair of components similarly placed with reference to the 

 carrier. All of these taken together form a pair of spectra or fre- 

 quency bands extending on either side from the carrier frequency 

 in the same way that the spectrum of the signal extends from zero 

 frequency. These bands of frequencies are spoken of as "side- 

 bands" and the component currents of these frequencies as " side- 

 band currents," or, more often, simply as " side-bands." The side- 

 band which extends upward in frequency from the carrier is called 

 the " upper side-band," and the other, which extends downward, the 

 " lower side-band." 



The form of these side-bands is shown schematically in Fig. 2, 

 where purely arbitrary curves are used to represent the amplitudes and 



AMPLITUDE AND PHASE 

 CHARACTERISTICS OF SIGNAL 



AMPLITUDE AND PHASE 

 CHARACTERISTICS OF SIDE-BANDS 



phases of the signal components over a limited frequency range. It 

 will be seen that the corresponding curves for the upper side-band 

 are derived from these by displacing them along the frequency axis 

 by the amount of the carrier frequency. The amplitude curve of the 

 lower side-band is derived by inverting that of the upper with respect 

 to the carrier frequency. For the phase curve of the lower side-band 

 that of the upper is to be similarly inverted and also reversed in sign. 



