No abstract

No abstract

Statistics of a synchronous binary message pulse train applied to a regenerative repeater are related to those of the original binary message, which is assumed ergodic. It is shown that the ensemble of possible message pulse trains is a nonstationary random process having a periodically varying mean and autocovariance. A spectral density is calculated which shows line spectral components at harmonics of the pulse rate and a continuous density function, both with intensity proportional to the square of the absolute value of the Fourier transform of the standard pulse at the frequency considered. The continuous component has many properties similar to thermal noise but differs in that, under certain conditions described, it can exhibit regularly spaced axis crossings, can be exactly predicted over finite intervals and is capable of producing discrete components when nonlinear operations are performed on it, even though no line spectral terms are originally present. The analytical results are applied to the problem of deriving a timing wave from the message pulse train by shock‐exciting a tuned circuit with impulses occurring at the axis crossings.

A new method of computing modulation products by means of multiple Fourier series is described. The method is used to obtain for the problem of modulation of a two-frequency wave by a rectifier a solution which is considerably simpler than any hitherto known.T HE problem of computing modulation products has 10Rg been recognized as being of fundamental importance in communication engineering. Heretofore certain quite fundamental modulation problems have been attacked by methods which are difficult to justify from the standpoint of mathematical rigor and some of the solutions obtained have been in the form of complicated infinite series that are not easy to use in practical computations. In this paper these problems are solved by means of a new method which is mathematically sound and whi~h yields results in a form well suited for purposes of computation.The analysis here given applies specifically to the case of two frequencies applied to a modulator of the" cut off" type; i.e., a modulator which operates by virtue of its being insensitive to input changes throughout a particular range of values. A simple rectifying characteristic forms a convenient basis of approximation for study of such modulators, and hence we consider in detail methods of calculating modulation in rectifiers when two frequencies are applied. Applications to certain other types of modulation problems and to the case of more than two applied frequencies are discussed briefly at the close. HALF WAVE LINEAR RECTIFIER-Two ApPLIED FREQUENCIESWe shall define a half wave linear rectifier as a device which delivers no output when the applied voltage is negative and delivers an output wave proportional to the applied voltage when the applied voltage is positive. We may take the constant of proportionality as unity since its only effect is to multiply the entire solution by a constant. Assume the input voltage e(L) to be specified by e(i) = P cos (pt + Op) + Q cos (qt + 0,).(1)The output wave will then consist of the positive lobes of the above function with the negative lobes replaced by zero intervals. It is 228

Methods of solution and specific results are given for the spectrum of the response of devices which have sharply defined transitions between conducting and non‐conducting regions in their characteristics. The input wave consists of one or more sinusoidal components and the operating point is adjusted by bias, which may either be independently applied or produced by the rectified output itself.