The Research Of Design Techniques For 2D FIR And Stable IIR Digital Filters

This paper considers the design of digital filters, mainly concentrates on the techniques for linear two dimensional (2D) FIR and stable IIR digital filters. The Minimax Design of 2D FIR Filters is not necessarily unique. In order to obtain a unique solution, we introduce some additional constraints to the Minimax design. This paper presents least total squared error design of 2D Minimax FIR Filters which is always unique. This unique Minimax solution can be obtained by using a quadratic programming with the primal-dual algorithm. A novel stability criterion based on complex analysis is proposed in this paper. The novel stability condition is both sufficient and necessary. The paper is arranged in four sections.The first section is introduction, mainly reviews the advantages and the recent research of 2D FIR and IIR digital filters. The introduction is about some algorithms of Minimax design and least squares design.The second section describes some definitions of 2D FIR and IIR digital filters. Then three kinds of criteria for digital filters design and the algorithms based on these criterias are given. The character of the algorithms is also presented in this section.The third section presents least total squared error design of 2D Minimax FIR filters. This section describes design of 2D Minimax FIR filters firstly, then gives the mixed objective function algorithm, introducing least total squared error to the objective function of Minimax design , that is, compromise between Minimax and least square design. Design examples with comparison are provided to demonstrate that the resulted filters are not only Minimax filter but also have least total squared error among Minmax filters. Then analyze compromise parameters on the results of the design filters. The fourth section focuses on introducing a stability criteria based on the complex analysis. Firstly , advantages and disadvantages of different stability criterias are described. Then the stability criteria proposed by the complex analysis is presented, which is necessary and sufficient for stability. A description of design criteria based on the weighted least squares is given and the new criteria was used as a stability constraints. Furthermore, Simulation shows that the application of this stability criteria can improve the performance of 1IR filter.