146 BELL SYSTEM TECHNICAL JOURNAL 



A special case of (4.10-9) occurs when noise alone is applied to a linear 

 rectifier. The low frequency portion of the output power spectrum is 



I -3 2 r 1 



-3-2 r 



+ 64V2'~""" (4-'«-'0) 



+ 2W3^""" + 



] 



where we have used (4.7-6) and Table 2 of Appendix 4C. 

 The correlation function of 



Vs = P cos pt -\- Q cos qt, 

 where p and q are incommensurable, is 



Jq{P^u- + z)- + 2uv cos />r) X Jo{Q\^U' -\- v- -{- luv cos ^r) 

 From equations (4.9-16) and (4.9-17) it is seen immediately that 



/%o =^ ~ I F{iu)MPu)MQu)e-'"'"^^° du (4.10-11) 



is the d.c. component of / when the applied voltage is 



P cos pt -\- Q cos qt + IV . (4.1-4) 



J. R. Ragazzini has obtained an approximate expression for the output 

 power spectrum when the voltage 



V = Vs+V^ 



(4.10-12) 

 Vs = Q(l -{- r cos pt)cos qt 



is impressed on a linear rectifier. In terms of our notation his expression 

 for the continuous portion of the power spectrum is (for low frequencies) 



(4.10-13) 



, . _ 1 ^, [Wcif) given by equation 



l^c(;) - _._./r.. , .., ^ X 1^^^ 5_j. 



7r2a^((22 -I- 2\^o) LC-^-S-l^) for square law device_ 



The a' is put in the denominator to cancel the a' in the expression (4.5-17). 

 We take the linear rectifier to be 



and replace the index of modulation, k, in (4.5-17) by r. 



^^ Equation (12), "The Effect of Fluctuation Voltages on the Linear Detector," Proc. 

 I.R.E., V. 30, pp. 277-288 (June 1942). 



