APPENDIX B 

 EFFECT OF A DETERMINISTIC LINE ON THE SPECTRUM 



Suppose that r]^ for 0_<n£N-l is a cosine curve. 



27Tmn TT 



(B-1) 



where 



wnere y is not necessarily an integer. What will be the effect on the 

 spectral density? The fast Fourier transform of n gives: 



N-1 

 % = ^t > a cos 

 nt-o 



2™0 N 



-i2Trmn/N 



N-1 



At Y [e^f^umo '^ - <i>) ^ e-i(2™o ^- <p) 



n=0 



-i2TTmn/N 



N-1 



aAt 

 2 



■i* X [e^^^^"'0''"^/^]. 



N-1 



n=0 '- J 



(B-2) 



Since, by the geometric series. 



l+r+r^+r2+...+ r^-l = (1 - rN)/(i - r] 



it follows that: 



% = 



aAt 



• ^ 1 . 3i2^(mo-m) .^ ^ _ ^-i2Tr(mo+m) 



2 _ gi2Tr(mQ-m)/N ^ _ -i27T(mg+m)/N 



(B-3) 



88 



