Linear phase paraunitary filter banks with unequal-length filters

This paper presents the theory, design, and efficient implementation of a new class of linear phase paraunitary filter banks (LPPUFB) which find application in transform-based image coding. These new LPPUFB have filters of different lengths: longer filters are kept for low-frequency components to prevent blocking, while shorter filters are reserved for high-frequency components to minimize ringing. The proposed lattice factorization structurally enforces the unequal-length property along with LP and PU properties, and it is robust under the quantization of lattice coefficients. Design and image coding examples are also presented to confirm the validity of the theory.