A Generalized Lapped Transform with Unequal Length Filters based on First-Order Linear-Phase Filter Banks

In this paper, we propose design methods for biorthogonal linear-phase filter banks (BOLPFBs) which have unequal length filters in their synthesis banks or in their both (analysis and synthesis) banks based on first-order linear-phase filter banks (FOLPFBs). First, we indicate that the building blocks in FOLPFBs can be used as those in variable-order LPFBs (VOLPFBs). Second, we propose a VOLPFB which have unequal length filters in its synthesis bank (UVLPFB). Long highpass filters of a synthesis bank often generate the ringing artifacts. Ringing artifacts are a main disadvantage in image coding based on FOLPFBs. Since UVLPFBs have long lowpass filters and short highpass filters in their synthesis bank, they can reduce the ringing artifacts as well as approximate smooth regions well.