e 
X 
= 
  
1 I X 
0 N 
Figure 4: fix) = gixed); 3X 211.2.,.... M. 
fix) = 0; Xx = Mel Mr2,....N. 
fig and c are periodic with period À s N. 
given in (2), (3) and (4). Also here, the different cases can be 
written in a common form 
M 
(9/30) (1/M) E c(x)f(x)g(xtu) = 
x=1 
M 2 2 
e C (8/340) H [cm Lc (x)g oe]; (35) 
x=1 
where H is a simple operator (H = 1*, hy *ud4).oif,,.as.for equation 5, 
we neglect the right hand side of equation (35) and also note that 
C(x)f(x) = f(x) for all values of x, we obtain in vector notation 
(8/80) £.U"q » (8/80) F.D'ä = O (36) 
where f, dj, U and D are defined in (9), (10) and (12) ;: According to 
this model, the image g is cyclically displaced a distance y, a 
procedure which of course introduces wrap-around. However, this 
effect 1s suppressed by the window c according to figure 4. It should 
be noted that (36) is not identical to (11), this due to the different 
definitions (30) and (8) of g(u). However, substituting N for M, all 
relations (12) to (21) are still valid. 
We can now recalculate the matching parameter yu for the images used 
earlier. The results for cyclic and noncyclic displacement are now 
identical (as they should be) and are presented in figure 2d. Although 
there are no longer any effects of wrap-around, the result is seen to 
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