NAFI TR-lUij-0 



Because of its simplicity, equation (ll) is particularly- 

 appealing. It clearly reveals the small signal suppression effect — 

 the dependence of the output SNR upon the square of the input SNR — • 

 which is characteristic of all non-linear detectors at low input SNR's 

 (k, pp 279-286; lU, pp 267 & 307). It also indicates the importance of 

 the "signal-processing" parameters, T and W. The general result in 

 equation (9) can be put in the form of the white noise result in equation 

 (11) by defining an appropriate equivalent noise bandwidth, viz. 





or 



w« 



_lrv(0 <!{]'_ fr;5(f)Jf] 



fr^'ui Jf 



Then equation 9 can be written as 



rt^M'off 



(6 L ^) 



S/vR^ ^ TWe 



I H^U^ 



Ja^ 



C^iOiij 



-o© 



= 7~ 



We (j;)'' (31) 



the 



■where S and N denote total input signal and noise powers - i.e., 

 result of integrating the input power spectra S(f) and N(f). 



There is precedence for introducing a definition such as 

 equation Bl: e.g., Blackman and Tukey (16, p 19 ff) xitilize this defini- 

 tion of equivalent width in their analysis of power spectra measurement. 

 Although Wg may appear to be an obscure method of defining bandwidth, 

 rewriting and manipulating equation Bl will reveal a physical interpre- 

 tation of the result. Thus 



- 2 





e<e 



— o* 





-i 



~ 2 





or 





