Design of linear phase with unequal length paraunitary filter banks with suboptimal coding gain

In this paper, we present a design of M-channel linear-phase paraunitary filter banks (LPPUFB), with filters of unequal lengths and same center of symmetry, (ULPPUFB) without using non-linear optimization algorithms. ULPPUFB can be viewed as generalized lapped orthogonal transforms (GenLOTs) with variable-length basis functions and are used in block transform-based image coding. ULPPUFB has long basis functions in order to avoid blocking artifacts, whereas it reserves short basis functions for high-frequency signal components like edges, thereby limiting ringing artifacts. The design of ULPPUFB has already been shown and can be expressed completely using a lattice structure. However, when it is used in image coding, the coding gain must be maximization, and then we must use non-linear optimization algorithms. When filter length or channel numbers are increased, non-linear optimization algorithms would necessitate an enormous amount of calculation. In this paper, we design each filter without using non-linear optimization, directly based on the compaction problem and implement ULPPUFB by changing these filters into lattice structures. Then, we show their validity.