Design of non-expansionist and orthogonal extension methods for tree-structured filter banks

Signal extension methods have been extensively used when applying filter banks to finite length sequences. However, not every extension guarantees perfect reconstruction without considering extra subband samples, that is, in some cases the associated transform is expansionist. In this paper we introduce first the most general method for designing signal extensions which yield non-expansionist subband transforms. Secondly, all orthogonal extension methods are constructed. We conclude by analyzing some examples of the new boundary filters associated to the proposed extensions