Characterization of regular linear-phase paraunitary filter banks using dyadic-based structures

We re-examine the design of structurally regular linear-phase (LP) paraunitary filter banks (PUFBs) via a general framework without the LP constraint, and show that by a suitable choice of parameterization, the general regularity theory simplifies significantly under the LP assumption. A new geometric condition for regularity is presented which is essentially equivalent to but simpler than that in Oraintara et al. (2001). A connection between the general-purpose dyadic-based building block and the order-one LP building block used in the GenLOT structure is established.

1. INTRODUCTION

Bold-faced characters denote either a column vector or a matrix. The th column of a matrix is denoted as . For is the unit vector of and are the -vectors of all ones and all zeros, respectively, and and denote the identity and reverse identity matrices, respectively. denotes the rank of . An constant matrix is said to be unitary if .