DocumentCode :
1231361
Title :
Design of linear-phase variable 2-D digital filters using matrix-array decomposition
Author :
Deng, Tian-Bo
Author_Institution :
Dept. of Inf. Sci., Toho Univ., Chiba, Japan
Volume :
50
Issue :
6
fYear :
2003
fDate :
6/1/2003 12:00:00 AM
Firstpage :
267
Lastpage :
277
Abstract :
A novel approach for designing linear-phase variable two-dimensional (2-D) digital filters is described, which is based on the matrix-array decomposition (MAD) of real-valued multidimensional arrays. By using the MAD, the desired variable 2-D magnitude response can be decomposed into the real-valued frequency response specifications of the normal zero-phase constant 2-D filters and the approximation specifications of multidimensional polynomials. Consequently, the problem of approximating the desired variable 2-D magnitude response can be decomposed into sub-problems that involve the design of zero-phase constant 2-D filters and the approximation of multidimensional polynomials. Once the zero-phase constant 2-D filters and the multidimensional polynomials are obtained, interconnecting them yields a zero-phase variable 2-D digital filter. Finally, a linear-phase variable 2-D digital filter can be easily obtained by simply modifying the zero-phase constant 2-D filters (noncausal) to linear-phase ones (causal) through shifting the filter coefficients. Since the sub-problems are much easier to solve than the direct approximation of the given variable 2-D magnitude specification, this MAD-based design approach is extremely efficient and straightforward. In designing zero-phase constant 2-D filters and approximating multidimensional polynomials, we also propose a new objective criterion for selecting appropriate filter orders and polynomial degrees. Furthermore, we also show that the resulting linear-phase variable 2-D filters have highly parallel structures and modularity, which are suitable for high-speed multidimensional signal processing. Two numerical examples are given to demonstrate the effectiveness of the MAD-based design approach.
Keywords :
frequency response; linear phase filters; matrix decomposition; multidimensional signal processing; polynomial approximation; two-dimensional digital filters; 2-D magnitude response; high-speed multidimensional signal processing; highly parallel structures; linear-phase variable 2-D digital filters; matrix-array decomposition; modularity; multidimensional polynomial approximation specifications; numerical examples; objective criterion; real-valued frequency response specifications; real-valued multidimensional arrays; zero-phase constant 2-D filters; zero-phase variable 2-D digital filter; Band pass filters; Cutoff frequency; Digital filters; Frequency response; Matrix decomposition; Multidimensional signal processing; Multidimensional systems; Polynomials; Signal design; Two dimensional displays;
fLanguage :
English
Journal_Title :
Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7130
Type :
jour
DOI :
10.1109/TCSII.2003.812913
Filename :
1209304
Link To Document :
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