CARRIER AND SIDE-BANDS IN RADIO TRANSMISSION 91 



be resolved. The use of these terms implies a point of view which 

 perhaps is employed less commonly in radio engineering than in some 

 of the other branches of the communication art. For this reason, 

 I shall, at the risk of repeating much that is already in the literature, 2 

 review such of the fundamentals of this viewpoint as are necessary 

 to an understanding of what is to follow. 



Analysis of a Signal Wave 



Briefly stated, the point of view is that any signaling wave may 

 be resolved into sustained sinusoidal components, which may be 

 thought of as traversing the system as individual currents and re- 

 combining at the receiving end to form the reproduced signal. The 

 possibility of such a resolution has been demonstrated mathematically 

 and the formulas for evaluating the amplitudes and phases of the 

 components are well known. A periodic wave may be expressed 

 as a Fourier series, that is, as the sum of an infinite series of com- 

 ponents the frequencies of which may be thought of as harmonics 

 of a fundamental frequency which is equal to the frequency of repeti- 

 tion of the wave. Such a resolution, however, is not directly ap- 

 plicable to the waves employed in communication, for by their very 

 nature they are not periqdic. A communication system must be 

 capable of transmitting any individual symbol regardless of what 

 precedes or follows it. We may, however, resolve such an aperiodic 

 wave by the mathematical device of assuming it to be one cycle of a 

 periodic wave in which the interval between successive occurrences 

 of the disturbance in question approaches infinity. The frequency of 

 repetition is then infinitesimal. The fundamental frequency of the 

 Fourier series and the frequency interval between adjacent compo- 

 nents are also infinitesimal; that is, the series of discrete lines of the 

 Fourier series spectrum merge into a continuous spectrum. Mathe- 

 matically this continuous spectrum is represented by the expression 



F(t) = ["s cos (qt + e) dq, ( 1 ) 



which is known as the Fourier integral. Physically we are to picture 

 this infiinte series of sustained sinusoids as having such amplitudes 

 and phases that the algebraic sum of their instantaneous values is 



2 "Carrier Current Telephony and Telegraphy," by E. H. Colpitts and O. B. 

 Blackwell; "Transactions of the American Institute of Electrical Engineers," 

 volume XL, page 205, 1921. "Application to Radio of Wire Transmission En- 

 gineering," by L. Espenschied; presented before The Institute of Radio Engineers, 

 January 23, 1922. 



