Design of 2-D linear phase digital filters using Schur decomposition and symmetries

Multidimensional Systems and Signal Processing

Volumn 15, Issue 1, 2004, Pages 65-81

  Aldhaheri, Rabah W ^a  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

Author keywords

2 D FIR filter; 2 D IIR filter, Schur decomposition method; Circularly symmetric; Cross Gramian matrix; Impulse response matrix; Octagonally symmetric; Symmetry in 2 D filters

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONTROLLABILITY; DESIGN; EIGENVALUES AND EIGENFUNCTIONS; IIR FILTERS; MATRIX ALGEBRA; TRANSFER FUNCTIONS; TWO DIMENSIONAL;

BALANCING TRANSFORMATION; CROSS-GRAMIAN MATRIX; IMPULSE RESPONSE MATRIX; LYAPUNOV EQUATION; OCTAGONALLY SYMMETRIC; SCHUR DECOMPOSITION METHOD;

FIR FILTERS;

EID: 0842278894     PISSN: 09236082     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:MULT.0000003933.41677.03     Document Type: Article

References (23)

1. T.S. Huang, J.W. Burnett, and A.G. Deczky, "The Importance of the Phase in Image Processing Filters," IEEE Trans. Acoust. Speech Signal Process., vol. ASSP-23, December 1975, pp. 529-542.
2. T.C. Speake and R.M. Mersereau, "A Note on the Use of Windows for Two-Dimensional FIR Filter Design," IEEE Trans. Acoust. Speech Signal Process., vol. ASSP-29, 1981, pp. 125-127.
3. J.H. McClellan, "Artifacts in Alpha-Rooting of Images," Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, April 1980, pp. 449-452.
4. P.K. Rajan and M.N.S. Swamy, "Design of Circularly Symmetric Two-Dimensional FIR Digital Filters Employing Transformations with Variable Parameters," IEEE Trans. Acoust., Speech Signal Processing, vol. ASSP-31, 1983, pp. 637-642.
5. P.K. Rajan and M.N.S. Swamy, "Quadrantal Symmetry Associated with Two-Dimensional Digital Transfer Functions," IEEE Trans. Circuits Syst., vol. CAS-25, 1978, pp. 340-343.
6. J.H. McClellan, "The Design of Two-Dimensional Filters by Transformation," Proc. 7th annual Princeton Conf. Information Sciences and Systems, 1973, pp. 247-251.
7. R.M. Mersereau, W.F.G. Meeklenbrauker, and T.F. Quatieri, "McClellan Transformation for Two-Dimensional Digital Filters: I-Design," IEEE Trans. Circuits Syst., vol. CAS-23, July 1976, pp. 405-413.
8. B.K. Lien, "On the Cascade Realization of 2-D FIR Filters Designed by McClellan Transformation," IEEE Trans. Signal Process., vol. 40, September 1992, pp. 2338-2340.
9. T. Lin, M. Kawamata, and T. Higuchi, "Design of Two-Dimensional Separable Denominator Digital Filters Based on the Reduced-Dimensional Decomposition," IEEE Trans. Circuits Syst., vol. CAS-34, August 1987, pp. 934-941.
10. G. Gu and B.A. Shenoi, "A Novel Approach to the Synthesis of Recursive Digital Filters with Linear Phase," IEEE Trans. Circuits Syst., vol. CAS-38, June 1991, pp. 602-612.
11. W.-P. Zhu, M.O. Ahmad, and M.N.S. Swamy, "Realization of 2-D Linear-Phase FIR Filters by Using the Singular-Value Decomposition," IEEE Trans. Signal Process., vol. 47, 1999, pp. 1349-1358.
12. R.E. Twogood and S.K. Mitra, "Computer-Aided Design of Separable Two-Dimensional Digital Filters," IEEE Trans. Acoustics., Speech, Signal Process., vol. ASSP-25, 1977, pp. 165-169.
13. T.-B. Deng and M. Kawamata, "Frequency-Domain Design of 2-D Digital Filters Using the Iterative Singular Value Decomposition," IEEE Trans. Circuits Syst., vol. CAS-38, 1991, pp. 1225-1228.
14. W.-S. Lu, H.-P. Wang, and A. Antoniou, "Design of Two-Dimensional Digital Filters Using the Singular-Value Decomposition and Balanced Approximation Method," IEEE Trans. Signal Process., vol. 39, October 1991, pp. 2253-2262.
15. S.A. Aly and M.M. Fahmy, "Symmetry in Two-Dimensional Rectangular Sampled Digital Filters," IEEE Trans. Acoust., Speech Signal Processing, vol. ASSP-29, 1981, pp. 794-805.
16. S.A. Aly and M.M. Fahmy, "Symmetry Exploitation in the Design and Implementation of Recursive 2-D Rectangularly Sampled Digital Filters," IEEE Trans. Acoust., Speech Signal Processing, vol. ASSP-29, 1981, pp. 973-982.
17. M. Ohki, M., Kawamata, and T. Higuchi, "Efficient Design of Two-Dimensional Separable Denominator Digital Filters Using Symmetries," IEEE Trans. Circuits Syst., vol. CAS-37, January 1990, pp. 114-120.
18. S.-C. Pei and J.-J. Shyu, "Symmetric Properties of 2-D Sequences and their Applications for Designing Linear-Phase 2-D FIR Digital Filters," Signal Processing, vol. 42, March 1995, pp. 261-271.
19. A.J. Laub, "A Schur Method for Solving Algebraic Riccati Equations," IEEE Trans. Autom. Control, vol. AC-24, June 1979, pp. 913-921.
20. R.W. Aldhaheri, "Model Order Reduction Via Real Schur form Decomposition," Int. J. Contr., vol. 53, March 1991, pp. 709-716.
21. R.W. Aldhaheri and N.B. Al-Hussaini, "Approximation of FIR by IIR Digital Filters Using Orthonormal Bases," Proc. Internat. Conf. On Information, Communication and Sig. Process., Singapore, vol. 3, 9-12 September 1997, pp. 1311-1314.
22. I. Kale, J. Gryka, G.D. Cain, and B. Beliczysnki, "FIR Filter Order Reduction: Balanced Model Truncation and Hankel-Norm Optimal Approximation," IEE Proc. Vis. Image Signal Process., vol. 141, no. 3, 1994, pp. 168-174.
23. B. Beliczynski, I. Kale, and G.D. Cain, "Approximation of FIR by IIR Digital Filters: An Algorithm Based on Balanced Model Reduction," IEEE Trans. Signal Process., vol. 40, March 1992, pp. 532-542.