Fig. 3.1. Shift of cross correlation in applying the lag window. 
This alignment technique can be expressed as a shift in lag windows as well as a 
shift in the origin of the correlation, or as a shift of the output time series relative to the 
input time series, 
re (N-1}-ro 
SAo)=— SS wr-ro)Rir)e“*”, (3.1) 
Cer ee (N-1)-ro 
where w(r) is the standard type of lag window for estimation of the auto—spectra. 
Thus 
; (N-1) 
S(O) =— > WORT + roe), (3.2) 
r=—(N-1) 
So if we set 
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