Notes on the Theory of Modulation*

It is a well-known fact that in carrier wave' transmission it is necessary to provide for the efficient transmission and reception not only of the carrier frequency itself but also for a band of frequencies of width depending on the frequency and character of the signal itself. This necessity is becoming more and more a serious consideration as the severity of wave length regulation and the necessity of sharp selective tuning are increased. In view of these facts a great deal of inventive thought has been devoted to the problem of narrowing the band of transmission frequencies. Some of the schemes which are directed to this end are very ingenious; all, however, are believed to involve a fundamental fallacy. It is the purpose of this note to discuss briefly the general problem of modulation and to analyze the more ingenious and plausible schemes which have been advanced to solve this problem. A pure modulated wave may be mathematically defined by the expression f(t) Acos (o (1) Here f(t) is the low frequency signal, o/2 ;r is the carrier frequency and A is an amplitude factor which fixes the magnitude of the transmitted wave. The pure modulated wave is often defined in words as "a carrier wave of constant frequency whose amplitude is proportional to the signal wave." Properly interpreted this definition is correct; however, the inference which is sometimes made, that the resultant wave is of constant frequency is erroneous, as may easily be shown. *Received by the Editor, January 6, 1922. 11t is to be understood that the term carrier wave is employed in its generic sense to cover radio as well as carrier wave wire transmission in both of which the carrier wave plays the sdtne role. 2See "Carrier Wave Telephony and Telegraphy," by Colpitts and Blackwell, "Journal of the American Institute of Electrical Engineers," April, 1921