Equation (A-13) is comparable in form to equation (7) in the text but has the 

 important difference that the frequencies are arbitrary. They are no longer 

 tied to the record length, but the convenience of orthogonality is generally 

 lost. Amplitude and phase for each frequency constituent are defined by 



Ai=Af 



+ ai 



(A-14) 



.-1 



which are comparable to equation (13) in the text. 



It is desirable to consider the x^'s specified in equation (A-11) in 

 pairs in the MRS analysis. This requires only minor modifications in the 

 procedure. Constituents are judged in pairs on the basis of a multiple 

 correlation with the time series defined as 



21-1 2^-' 



(I 



21-1 



-.y. 



il ^2iy> 



I x|,_^ I y2 I x2, I y2 



1 - 



I ^ii-1 I ^l± I y' 



(A-15) 



(I 



21-1 21 



y x2. y x2. 



L ^2i-l ^ 2i 



-1 



The switching of columns and the switching of rows, shown in equations 

 (A-9) and (A-10), are done in pairs rather than singly. The solution of a 

 column and orthogonalization of remaining columns is done twice in succession 

 to solve for both g and a of the selected frequency. Then equation (A-15) 

 is computed for all remaining constituents to again identify the maximum. The 

 procedure is continued for as many steps as desired. 



82 



