New orthogonal extension methods for tree-structured filter banks

When processing finite length sequences via paraunitary filter banks, a commonly used technique consists of artificially extending the signal before the analysis stage. The use of the extension methods avoids the border effects, and perfect reconstruction, even orthogonal, size-limited filter banks can be defined. In this paper we first characterize and generate all signal extension methods which yield orthogonal subband transforms. Secondly, the particular case of non-circular orthogonal extension methods is investigated, and the first general design method of non-circular orthogonal extensions is derived. Finally, the computational cost of the design algorithm is evaluated and compared to that of orthogonal boundary filter generation methods.