TM No. 377 



The in-phase correlation of the tvo records is given by: 



EGO - ^ [pa) +• c co] • 



The out-of~phase correlation of the two records is given by: 



PC 1 -) -- ^[dco-cco] . 



The in^phase energy spectrum or co-spectrum is approximated by; 



(111=46) 



(111-1*7) 



2(k) -- 



M 



M 





. (III-W) 



The out-of -phase or qua-=spectrum is given by; 



(111-1+9) 



The estimate of the coherence (see equation (III-3I+)) is given by; 



where Vu(K) and Vw(jK) are the auto=spectra of the "^ and (^ series in the form 

 of equation (111-41), 



The phase lead of the function 'Uy, over £<</■>, is given by: 



(h) (K) - ARcmw 





(hi- 51) 



Finally, the linear correlation coefficient, formed from equation ( 111=29) ^ 

 is of the form: 



ttu CK) =^ 



e(o) 



where ^Xo) and A w (,o)are the auto-covariance functions of vl and w at zero 

 lag (given by equation ! III- 1 +6)). 



(111-52) 



61 



