266 BELL SYSTEM TECHNICAL JOURNAL 



rangements designed to eliminate static interference. Work on this 

 prolilem has been for the most part futile, on account of the lack of a 

 clear anahsis of the problem and a failure to perceive inherent limi- 

 tations on its solutions by means of selective circuits. 



The object of this paper is twofold: (1) To develop the mathe- 

 matical theory of the behavior of selective circuits when subjected 

 to random, irregular disturbances, hereinafter defined and designated 

 as random interference. This will include a formula which is pro- 

 posed as a measure of the figure of merit of selective circuits witk respect 

 la random interference. (2) On the basis of this theory to examine 

 the problem of static interference with particular reference to the ques- 

 tion of its elimination by means of selective circuits. The mathe- 

 matical theory shows, as might be expected, that the complete solu- 

 tion of this problem requires experimental data regarding the fre- 

 quency distribution of static interference which is now lacking. On 

 the other hand, it throws a great deal of light on the whole problem 

 and supplies a formula which furnishes the theoretical basis for an 

 actual determination of the spectrum of static. Furthermore, on 

 the basis of a certain mild and physically reasonable assumption, 

 it makes possible general deductions of practical value which are 

 certainly qualitatively correct and are believed to involve no quanti- 

 tatively serious error. These conclusions, it may be stated, are in 

 general agreement with the large, though unsystematized, body of 

 information regarding the behavior of selective circuits to static 

 interference, and with the meagre data available regarding the wave 

 form of elementary static disturbances. 



The outstanding conclusions of practical value of the present 

 study may be summarized as follows : 



(1) Even with absolutely ideal selective circuits, an irreducible 

 minimum of interference will be absorbed, and this minimum in- 

 creases linearly with the frequency range necessary for signaling. 



(2) The wave-filter, when properly designed, approximates quite 

 closely to the ideal selective circuit, and little, if any, improvement 

 over its present form may be expected as regards static interference. 



(3) As regards static or random interference, it is quite useless to 

 employ extremely high selectivity. The gain, as compared with 

 circuits of only moderate selecli\ity, is \'ery small, and is inevitably 

 accompanied by disadvantages such as sluggishness of response with 

 consequent slowing down of the possible speed of signaling. 



(4) By aid of a simple, easily computed formula, it should be pos- 

 sible to determine experimentally the frequency spectrum of static. 



