The Statistical Energy-Frequency Spectrum of Random Disturbances

N a paper entitled "Selective Circuits and Static Interference" {B. S. T. / . , April, 1925) the writer discussed the "energyfrequency spectrum" (hereinafter precisely defined) of irregular random disturbances extending over a long interval of time. In view of our lack of even statistical information regarding static or atmospheric disturbances the specification of the energy-frequency spectrum, denoted by R(gj), was necessarily qualitative, and it was merely postulated that " R(co) is a continuous finite function of co which converges to zero at infinity and is everywhere positive. It possesses no sharp maxima or minima and its variation with respect to co(co = 2irf), where it exists, is relatively slow." In a paper entitled "The Theory of the Schroteffekt," 1 T. C. Fry deals with a similar problem, namely, the energy or "noise" absorbed in a vacuum tube from a stream of electrons with random time distribution. His method of attack is widely different from that of the present paper. In a more recent paper on "The Analysis of Irregular Motions with Applications to the Energy-Frequency Spectrum of Static and of Telegraph Signals" (Phil. Mag., Jan., 1929), G. W. Kenrick, by making certain hypotheses regarding the wave-form of the elementary disturbances whose aggregate is supposed to represent static interference, and by applying probability analysis, arrives at explicit formulas for the "statistical" or "expected" value of i?(co) for a number of different cases. I In the present paper the statistical or "expected" energy-frequency spectrum R(u) of random disturbances is investigated by a method which is believed to be somewhat more general and direct than that of Kenrick.2 The results are applicable to the Schroteffekt, telegraph Jour.