NAFI TR-lUliO 



VP. 



where K = Q . The only way that equation 23 can be valid for all values 

 of y{f), which is an arbitrary function, is if 



r.(f)| = 1^ 



A//(f) 



U1) 



Since K is a scalar constant, it acts merely as a scale factor which can 

 have no effect upon the optimum specification of r(f ); thus, it can be 

 arbitrarily chosen as unity, resulting in the specification of equation 19- 

 Using the Eckart filter for jr(f)| , the spectra into the square- 

 law device become 



m) '- 





By substitution into equation 10 (or 9), the output SNE takes the simple 

 form ' *^** r '^z // ) 1 2 



utilizing the same spectral forms assumed in Section h, but ex- 

 tending the high frequency response to infinity, the input signal and 



(20 



noise spectra are 





;(o-j 



Af 





V <o 



we have . t ' 



S,: (jl - A f-t 



where § = P-a, as in Section h. 



Substituting equation 28 into 26 and integrating, the output SNE 

 for an infinite bandwidth Eckart filter is 





s«^;^=«)= T(|) ^T^j /; 



; 



?>t 



(Z't) 



19 



