Biomedical Engineering Reference
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and.for.any.particular.
Z
.(note:.
Z
.can.be.
Z
odd
.or.
Z
even
),.we.have.the.follow-
ξ
∈
n
ing.two.different.cases:
.
a.. For. any. pasting. position.
k
,. which. makes. some. actual. bits. of. ξ . be.
located.in.
V
k
,.it.is.possible.to.lip.the.rightmost.bit.in.
V
k
.to.ind.a.cor-
responding.
ξ
∈
Z
′
.such.that
n
′
∆ ξ
(
,
V
′ ξ
;
,
V
′ = ∆ ξ
)
(
,
V
′ ξ
;
,
V
′
).
.
i
k
n
k
i
k
n
′
k
.
.
. Hence,.if.there.are.some.actual.bits.of.ξ
i
.located.in.
V
k
,.the.differ-
ence.term.in
.
Equation.(A.16)
.
is.zero,.that.is,
∑
∑
∆ ξ
(
,
V
′ ξ
;
,
V
′ −
)
∆ ξ
(
,
V
′ ξ
;
,
V
′
)
=
0
i
k
n
k
i
k
n
k
ξ
∈
Z
ξ
∈ ′
Z
.
.
n
n
.
b.. For. any. pasting. position.
k
,. which. makes. all. the. actual. bits. be.
located. in.
V
k
′ . only. when.
ξ
= ξ ,.
∆ ξ
(
,
V
′ ξ
;
,
V
′ =
) 1
;. otherwise,.
n
i
i
k
n
k
∆ ξ
(
,
V
′ ξ
;
,
V
′ =
) 0
..We.deine.a.set.
K
′:
i
k
n
k
K
'.= {
k
:.no actual bit in pasting region}.
For.any.
k
∈
K
',.we.have
∆ ξ
(
,
V
;
ξ
,
G
) 1
=
.
i
k
m
c k
,
.
and
1,
1,
ξ ∈
Z
Z
∑
∑
i
∆ ξ
(
,
V
′ ξ
;
,
V
′ −
)
∆ ξ
(
,
V
′ ξ
;
,
V
′
)
=
i
k
n
k
i
k
n
k
−
ξ ∈
′
i
ξ
∈
Z
ξ
∈ ′
Z
.
.
n
n
Figure.A.4
.
helps.clarify.cases.a.and.b.
By.summing.cases.a.and.b,.we.have
L L
−
g
∑
∑
∑
∑
( )
i
( )
i
a
−
a
= ±
K
1
mn
mn
ξ
∈
Z
ξ
∈ ′
Z
c
=
0
k K
∈
′
n
n
N
L L
0
= ±
−
−
1
g
≡
C
.
row
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