Two-Dimensional Symmetric Half-Plane Recursive Doubly Complementary Digital Lattice Filters
This paper deals with the problem of two-dimensional (2-D) recursive doubly complementary (DC) digital filter design. We present a structure of 2-D recursive DC filters by using 2-D symmetric half-plane (SHP) recursive digital all-pass lattice filters (DALFs). The novelty of using 2-D SHP recursive DALFs to construct a 2-D recursive DC digital lattice filter is that the resulting 2-D SHP recursive DC digital lattice filter provides better performance than the existing 2-D SHP recursive DC digital filter. Moreover, the proposed structure possesses a favorable 2-D DC half-band (DC-HB) property that allows about half of the 2-D SHP recursive DALF’s coefficients to be zero. This leads to considerable savings in computational burden for implementation. To ensure the stability of a designed 2-D SHP recursive DC digital lattice filter, some necessary constraints on the phase of the 2-D SHP recursive DALF during the design process are presented. Design of a 2-D diamond-shape decimation/interpolation filter is presented for illustration and comparison.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1124631Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 855
 Sanjit K. Mitra, “Digital signal processing: a computer-based approach”, New York: Mc-Graw Hill, 1998.
 P. A. Regalia, S. K. Mitra and P. P. Vaidyanathan, “The digital all-pass filter: a versatile signal processing building block”, Proc. of IEEE, pp. 19-37, vol. 76, no. 1, Jan. 1988.
 P. Vaidyanathan, P. Regalia, S. K. Mitra, “Design of doubly complementary IIR digital filters using a single complex allpass filter, with multirate applications”, IEEE Trans. on Circuits and Systems, vol. 34, no. 4, pp. 378 –389, Apr. 1987.
 H. Johansson and T. Saramaki, “A class of complementary IIR filters”, IEEE Int. Sym. on Circuits and Systems, vol. 3, pp. 299 –302, June 1999.
 P. P. Vaidyanathan, Multirate Systems and Filter Banks, New Jersey: Prentice Hall, 1992.
 P. P. Vaidyanathan, “Passive Cascaded-Lattice Structures for Low-Sensitivity FIR Filter Design, with Applications to Filter Banks,” IEEE Transactions on Circuits and Systems, vol. CAS-33, no. 11, pp. 1045-1064, Nov. 1986.
 A. H. Gray, Jr. and J. D. Markel, “Digital lattice and ladder filter synthesis,” IEEE Transactions on Audio and Electroacoustics, vol.21, no.6, pp.491-500, Dec. 1973.
 S. Y. Kung, B. C. Levy, M. Morf, and T. Kailath, "New results in 2-D systems theory, part II: 2-D state space models – realization and the notions of controllability, observability and minimality," Proc. IEEE, vol. 65, no. 6, pp. 945-961, June 1977.
 G. E. Antoniou, “2-D lattice discrete filters: minimal delay and state space realization,” IEEE Signal Processing Letters, vol. 8, no. 1, pp. 23-25, Jan. 2001.
 J.-H. Lee and Y.-H. Yang, “Two-channel quincunx QMF banks using two-dimensional digital allpass filters,” IEEE Trans. on Circuits and Systems – I, vol. 56, no. 12, pp. 2644-2654, Dec., 2009.
 D. E. Dudgeon and R. M. Mersereau, Multidimensional Digital Signal Processing, New Jersey: Prentice Hall, 1984.
 S.-C. Pei and J.-J. Shyu, “Eigenfilter design of 1-D and 2-D IIR digital all-pass filters,” IEEE Trans. Signal Processing, vol. 42, no. 4, pp. 966-968, Apr. 1994.
 T. Steihaug, “The conjugate gradient method and trust regions in large scale optimization,” SIAM Journal on Numerical Analysis, vol. 20, no. 3, pp. 626-637, June 1983.
 J. Nocedal and S. J. Wright, Numerical optimization, New York: Springer–Verlag, 1999.
 E. Dubois, “The sampling and reconstruction of time-varying imagery with application in video systems,” Proc. IEEE, vol. 73, no. 4, pp. 502-522, Apr. 1985.
 P. Carrai, G. M. Cortelazzo, and G. A. Mian, “Characteristics of minimax FIR filters for video interpolation/decimation,” IEEE Trans. Circuits and Systems for Video Technol., vol. 4, no. 5, pp. 453-467, Oct. 1994.
 J.-H. Lee and Y.-H. Yang, “Design of 2-D interpolation/decimation filters using a general 2-D digital allpass filter,” Digital Signal Processing, vol. 22, no. 5, pp. 847-858, Sept. 2012.