Optimal design of triplet halfband filter banks via Semidefinite Programming

This paper proposes a computationally efficient method for designing a class of triplet halfband filter banks. We show that the design of perfect reconstruction two-channel Alter banks with arbitrary regularity order can be precisely formulated as a semi-definite programming problem. We also show that the dual problem has a significant smaller number of variables and, hence, can be solved efficiently. The effectiveness of the proposed method is demonstrated by the design examples of filter banks with high filter order and arbitrary regularity order.