Passive, active, and digital filters (3ed., CRC, 2009) - tiera.ru

1-D Multirate Filter Banks 24-332Analysis sidec 1s 1c Lc 0s 0s LZ –1 c 0–s 0Z –1–s 0–s 1–s L2c 0 c 1Z –1c LSynthesis sidec Lc L–s Ls Lc 1–s 1s 1c 1c k = cos θ kZc 0S k = sin θ ks 022 +FIGURE 24.19Orthogonal lattice structure.whereD(z) 1 00 z 1and S i 1 a ia i 1and a i 6¼ 0 are the free parameters that define the filters. The structure here is similar to theorthogonal lattice structure except for a sign change in one of the element of S i .2. Type B: where all filters in the bank have odd length. All filter coefficients are then symmetric.The polyphase matrix is given bywhereB i (z) ¼E(z) ¼ YLi¼1B i (z) (24:97)1 þ z 1 a i1 þ b i z 1 þ z 2 a i (1 þ z 1 )and a i 6¼ 0, b i 6¼ 2 are the free parameters that define the filters.This structure can be used to implement all of the linear-phase odd-length wavelet filter banksdiscussed in Sections 24.6.3, 24.6.5, and 24.6.6, such as the (5,3), (7,5), (9,7), and (19,13)-tap filtersand their inverses.24.8.4 Lifting SchemeThe basic idea behind lifting [17–19] is simple:Whatever change was performed to the signal by some process of addition can be undone by theequivalent process of subtraction.