Lattice Structure Realization for The Design of 2-D Digital Allpass Filters With General Causality

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 64; no. 2; pp. 419 - 431
• Main Authors: Lee, Ju-Hong, Du, Jiun-Shian
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Alloys; Circuit stability; Delays; Design optimization; Digital allpass filter (DAF); Hardware; lattice structure; Lattices; minimal realization; Minimax technique; Stability criteria; State space models; Transfer functions; Two dimensional models; wedge-shaped support region
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2016.2604678

This paper presents a lattice structure for the realization of two-dimensional (2-D) recursive digital allpass filters (DAFs) with general causality. We employ four basic lattice sections to realize 2-D recursive DAFs with wedge-shaped coefficient support region like a nonsymmetric half-plane (NSHP) support region. The theory and transfer functions of the realized 2-D lattice DAFs are derived. Some variations of the 2-D lattice structure are also presented. We use the Roesser state space model to verify the minimal realization of the proposed 2-D recursive lattice DAF. We present a least-squares design technique and a minimax design technique to solve the nonlinear optimization problems of the proposed 2-D lattice DAF structure. The novelty of the presented lattice structure is that it not only inherits the desirable attributes of 1-D Gray-Markel lattice allpass structure but also possesses the advantage of better performance over the existing 2-D lattice allpass structures. Finally, several design examples are provided for conducting illustration and comparison.