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Two‐dimensional recursive digital filters with nearly circular‐symmetric magnitude response and approximately linear phase
Author(s) -
Lee JuHong,
Yang YuanHau
Publication year - 2011
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.697
Subject(s) - minimax , mathematics , cascade , digital filter , linear phase , block (permutation group theory) , filter (signal processing) , linear filter , connection (principal bundle) , phase (matter) , phase response , control theory (sociology) , topology (electrical circuits) , combinatorics , computer science , physics , mathematical optimization , geometry , engineering , control (management) , quantum mechanics , chemical engineering , artificial intelligence , computer vision
This paper presents a general structure using 1‐D and two‐dimensional (2‐D) recursive digital all‐pass filters (DAFs) for the design of 2‐D recursive circularly symmetric digital low‐pass filters (CS‐DLFs). The general structure is a cascade of two stages composed of all‐pass building blocks. The first stage is a parallel connection of a 2‐D recursive DAF with a symmetric half‐plane (SHP) support for its filter coefficients and a 2‐D pure delay block. The second stage composed of a parallel connection of a 1‐D recursive DAF and a 1‐D pure delay block is used for eliminating the unwanted pass‐band induced by the first stage. As a result, the design of a 2‐D CS‐DLF in either the least‐squares or the minimax sense can be formulated in a simple linear optimization problem in terms of the weighted‐phase response error for each DAF. Design results with nearly circularly symmetric magnitude response and approximately linear phase are also provided for illustration and comparison. Copyright © 2010 John Wiley & Sons, Ltd.