Orthogonal PR Filterbanks The FIR perfect-reconstruction (PR) conditions leave some freedom in the choice of H 0 z and H 1 z . Orthogonal PR filterbanks are defined by causal real-coefficient even-length-N analysis filters that satisfy the following two equations: 1 H 0 z H 0 z H 0 -z H 0 z H 1 z ± z N 1 H 0 z To verify that these design choices satisfy the FIR-PR requirements for H 0 z and H 1 z , we evaluate H z under the second condition above. This yields H z ± H 0 z H 1 z H 0 -z H 1 z z N 1 H 0 z H 0 z H 0 -z H 0 z z N 1 which corresponds to c -1 and l N 1 in the FIR-PR determinant condition H z c z l . The remaining FIR-PR conditions then imply that the synthesis filters are given by G 0 z -2 H 1 z 2 z N 1 H 0 z G 1 z 2 H 0 z 2 z N 1 H 1 z The orthogonal PR design rules imply that H 0 ω is "power symmetric" and that H 0 ω H 1 ω form a "power complementary" pair. To see the power symmetry, we rewrite the first design rule using z ω and -1 ± π , which gives 1 H 0 ω H 0 ω H 0 ω H 0 ω H 0 ω 2 H 0 ω 2 H 0 ω 2 H 0 ω 2 The last two steps leveraged the fact that the DTFT of a real-coefficient filter is conjugate-symmetric. The power-symmetry property is illustrated in :

Power complementarity follows from the second orthogonal PR design rule, which implies H 1 ω H 0 ω . Plugging this into the previous equation, we find 1 H 0 ω 2 H 1 ω 2 The power-complimentary property is illustrated in :