
For FullText PDF, please login, if you are a member of IEICE,
or go to Pay Per View on menu list, if you are a nonmember of IEICE.

Design of TwoDimensional Recursive Digital Filters Based on the Iterative Singular Value Decomposition
Tianbo DENG Masayuki KAWAMATA
Publication
IEICE TRANSACTIONS (19761990)
Vol.E73
No.6
pp.882892 Publication Date: 1990/06/25
Online ISSN:
DOI:
Print ISSN: 00000000 Type of Manuscript: PAPER Category: Digital Signal Processing Keyword:
Full Text: PDF(838.8KB) >>Buy this Article
Summary:
In the design of twodimensional digital filters (2 DDF's), if the given 2 DDF design specifications can be decomposed into onedimensional 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 oneinput/multioutput 1 DDF and the other is that of a multiinput/oneoutput 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.

