i
i
i
i
i
i
i
i
140 7 Directional Wavelet Transform
taken as a linear combination of the even polyphase samples identified by the arrows
in Figure 7.1, specifically
P
e
(m,n) =
∑
i
α
i
x
e
(m + sign(i −1)tanθ
v
,n + i), (7.3)
where sign(x) is 1 for x ≥ 0 and -1 otherwise. The weight α
i
are given by the filter
taps. Note that x
e
(m+sign(i −1)tanθ
v
,n + i) is not necessarily sampled at an integer
position. The corresponding finite impulse response function in z domain is
P(z
1
,z
2
) =
b
∑
i=a
α
i
z
sign(i−1)tan θ
v
i
z
i
2
. (7.4)
Here, the indexes a and b delimit the finite support of the FIR wavelet filter. Since the
prediction is still calculated from the even polyphase samples, if the angle is known,
the ADL can still perfectly reconstruct the odd polyphase samples with Eq. (7.2).
In the updating ...