NAFI TR-l¥+0 



(1) the input signal and noise are members of stationary Gaussian 

 random processes, independent of one another, and 



(2) the input noise is "wide band" compared to the output filter. 



For the remainder of this paper, the output smoothing filter 

 is chosen to be a perfect, finite time averager with impulse response 



-{ 





Then (10, 15) 



Thus, for this output filter, the expression for the output SNR may be 

 written as 



_T [.C^mr 



A A 



If single sided power spectra, S(f) and W(f), are used in place 

 of the double sided S(f) and N(f), the resulting expression is 



Sfl/R -T <• ° — — 0«) 



S/VR.-T f-f^yy»4f 



as shown in Appendix A. 



If the noise is white over a band W, it is a straightforward 

 process to shov that equation 10 (or 9) reduces to 



iNK^' TWf^j^ (II) 



where S sind N are the signal and noise power (total power, not spectral levels) 

 into the square-law device.* 



*See Appendix B for a generalization of equation (ll). 



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