Abstract
In designing two-dimensional (2-D) digital filters in the frequency domain, an efficient technique is to first decompose the given 2-D frequency domain design specifications into one-dimensional (1-D) ones, and then approximate the resulting 1-D magnitude specifications using the well-developed 1-D filter design techniques. Finally, by interconnecting the designed 1-D filters one can obtain a 2-D digital filter. However, since the magnitude responses of digital filters must be nonnegative, it is required that the decomposition of 2-D magnitude specifications result in nonnegative 1-D magnitude specifications. We call such a decomposition the nonnegative decomposition. This paper proposes a nonnegative decomposition method for decomposing the given 2-D magnitude specifications into 1-D ones, and then transforms the problem of designing a 2-D digital filter into that of designing 1-D filters. Consequently, the original problem of designing a 2-D filter is significantly simplified.
This is a preview of subscription content, log in via an institution to check access.
References
T. Hinamoto and S. Maekawa, “Separable-Denominator 2-D Rational Approximation via 1-D Based Algorithm,”IEEE Trans. Circuits Syst., vol. CAS-32, October 1985, pp. 989–999.
L.F. Chaparro and G. Shufelt, “Least-Squares Design of Two-Dimensional Recursive Filters with Specified Magnitude and Linear Phase,”J. Franklin Inst., vol. 321, no. 4, April 1986, pp. 241–249.
S. Treitel and J.L. Shanks, “The Design of Multistage Separable Planar Filters,”IEEE Trans. Audio Electroacoust., vol. AU-20, October 1972, pp. 249–257.
T. Lin, M. Kawamata, and T. Higuchi, “Design of 2-D Separable-Denominator Digital Fitlers Based on the Reduced-Dimensional Decomposition,”IEEE Trans. Circuits Syst., vol. CAS-34, August 1987, pp. 934–941.
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.
T.-B. Deng and M. Kawamata, “Design of Separable-Denominator 2-D Digital Filters Using the Reduced Dimensional Decomposition Model,”Multidimensional Systems and Signal Processing, vol. 3, no. 1, March 1992, pp. 89–96.
R. E. Twogood and S.K. Mitra, “Computer-Aided Design of Separable Two-Dimensional Digital Filters,”IEEE Trans. Acoustics, Speech, Signal Processing vol. ASSP-25, April 1977, pp. 165–169.
A. Antoniou and W.-S. Lu, “Design of Two-Dimensional Digital Filters by Using the Singular Value Decomposition,”IEEE Trans. Circuits Syst., vol. CAS-34, October 1987, pp. 1191–1198.
M. Ohki and M. Kawamata, “Design of Parallel Separable Three-Dimensional Digital Filters for Frequency Domain Specifications,”Trans. IEICE Japan, vol. J72-A, August 1989, pp. 1247–1252.
T.-B. Deng, J. Murakami, and Y. Tadokoro, “A Novel Nonnegative Decomposition Method Applicable to 2-D Digital Filter Design,”Proc. 5th Karuizawa Workshop on Circuits Syst., Karuizawa, Japan, April 1992, pp. 237–242.
T.-B. Deng and M. Kawamata, “Design of Separable-Denominator Two-Dimensional Digital Filters Based on the Reduced-Dimensional Decomposition of Frequency Domain Specifications,”Trans. IEICE Japan, vol. J72-A, September 1989, pp. 1392–1399.
W.-S. Lu and A. Antoniou, “Design of 2-D Digital Filters with Arbitrary Amplitude and Phase Responses by Using the Singular Value Decomposition,”Proc. IEEE Symp. Circuits Syst., Singapore, June 1991, pp. 618–621.
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, October 1991, pp. 1225–1228.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Deng, TB., Soma, T., Murakami, J. et al. A novel nonnegative decomposition method and its application to 2-D digital filter design. Multidim Syst Sign Process 5, 97–119 (1994). https://doi.org/10.1007/BF00985865
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00985865