MATHEMATICAL ANALYSIS OF RANDOM NOISE 291 



Curves showing the probability density and distribution function of R, 

 when Q = 0, for various ratios of P/r.m.s. Iff are given. 



10. In section 3.11 it is pointed out that the representations (2.8-1) 

 and (2.8-6) of the noise current as the sum of a great number of sinusoidal 

 components are not the only ones which may be used in deriving the results 

 given in the preceding sections of Part III. The shot effect representation 



/(0^= 2 Fit - O 



—00 



studied in Part I may also be used. 



Part IV — Noise Through Non-Linear Devices 



1. Suppose that the power spectrum of the voltage V applied to the 

 square-law device 



I = aV^ (4.1-1) 



is confined to a relatively narrow band. The total low-frequency output 

 current It( may be expressed as the sum 



la = Ida + Iff (4.1-2) 



where Idc is the d.c. component and !(/ is the variable component. When 

 none of the low-frequency band is eliminated (by audio frequency filters) 



la = "f (4.1-6) 



where R is the envelope of V. If V is of the form 



V = V If ■{- P cos pt -{- Q cos qt, (4.1-4) 



where Fat is a noise voltage whose mean square value is ^o , then 



ll,=a' hi + P'h + OVo + ^'] (4.1-16) 



2. If instead of a square-law device we have a linear rectifier, 



1 = 1^ ^<^ (42-1) 



^ \aV, V>0 ^^-^ ^^ 



the total low- frequency output is 



lU = - (4.2-2) 



