Design of Two-Dimensional Recursive Digital Filters Based on the Iterative Singular Value Decomposition

Tian-bo DENG  Masayuki KAWAMATA  

IEICE TRANSACTIONS (1976-1990)   Vol.E73   No.6   pp.882-892
Publication Date: 1990/06/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Digital Signal Processing

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In the design of two-dimensional digital filters (2 DDF's), if the given 2 DDF design specifications can be decomposed into one-dimensional digital filter (1 DDF) specifications, the 2 DDF design problems can be reduced to 1 DDF ones. Thus the 2 DDF design problems can be made simpler. However, in the frequency domain design, the conventional decomposition methods can not avoid the problem that the 1 DDF magnitude specifications obtained from 2 DDF magnitude specification decomposition are not always nonnegative. Since negative values can not be regarded as magnitude specifications, design problem become intricate. Therefore, it is desirable in practice to develop a 2 DDF magnitude decomposition method which can guarantee the resulting 1 DDF magnitude specifications to be always nonnegative. Unfortunately, up to now, no such a method has ever been proposed. In this paper, we propose a new decomposition method called the Iterative Singular Value Decomposition (ISVD) for the decomposition of the given 2 DDF magnitude specification matrix. By the ISVD, the prescribed 2 DDF magnitude specification is decomposed into a pair of 1DDF ones, one of which is the magnitude response of a one-input/multi-output 1 DDF and the other is that of a multi-input/one-output 1 DDF. The ISVD guarantees that the resultant 1 DDF magnitude specifications are always nonnegative. The problem of designing a 2 DDF is then simplified through designing a pair of 1 DDF's with different delay elements. In our design method, 1 DDF's are designed by utilizing nonlinear optimization method to minimize the weighted magnitude square error functions. In the optimization process, a variable substitution method is proposed for transforming constrained optimization problems to unconstrained ones. As a result, no attentions should be paid to 1 DDF stability during the optimization process, and the stability of the resulting 1 DDF's is ensured. Three design examples are given to illustrate the effectiveness of the proposed method.