Design of symmetric bi-orthogonal double density wavelet filter banks

We look at the design of a class of oversampled filter banks and the resulting framelets. The oversampled property is achieved via an extra subband resulting in Double Density Filter Banks (DDFB’s). We design a class of such filters with linear phase property. We will look at a special class of framelets from a filter bank perspective, in that we will design double density filter banks (DDFB’s) as shown in Figure 1. We define type 1 polyphase representation as (1) and type 2 polyphase representation as (2) Given the following polyphase matrices: