Ni(f) - noise power spectrum at the input to the shaping 

 filter (Eqn. 2, Fig. 2). 



S(R,f ), S(f ) - signal power spectrum at the input of the 

 square -law device (Eqn. I3, Fig. 2) 



r(f )| - square of the transfer function of the shaping 

 filter (Eqn. I3, Fig. 2). 



A- this symbol over a power spectriim, e.g. S(f), denotes 

 single sided spectra (Eqn. lO). Generally^ double sided spectra are 

 used in derivations while single sided spectra are used to obtain 

 numerical results. See Appendix A. 



Of - Power of the frequency dependence of the signal spectra^ 

 i.e., Si(f)=Af'^ (Eqn. 12). 



N(f) - noise power spectrum at the input of the square-law 

 device (Eqn. 5j Fig- ''?-)• 



3 - power of the frequency dependence of the noise spectra, 

 i.e., Ni(f)=Bf° (Eqn. 12). 



£ ^ P-a - referred to as the relative signal spectral slope; 

 the signal spectra has a slope of -10 log 2 db/oct. w.r.t. the input 

 noise spectra (Eqn. 15)- 



§0 - refers to the mismatched Eckart filter: §0 is the 

 signal slope designed for, '•liich is not necessarily the actual signal 

 slope § (Eqn. Ul and ^2). 



T - the integration time associated with the output sranothing 

 filter (Eqn. 9 and preceding discussion) 



f\ - lower frequency limit of operating band; spectra are all 

 assumed to be zero below this value (Eqn. 12), 



W - the bandwidth of bandlimited systems: thus, the operating 

 band extends from fi to fi + W (Eqn. 12). 



— W / N 



IJ- ss - - normalized bandwidth variable (Eqn. 17 j- 



VI 



