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Design of Two-Channel Quincunx Quadrature Mirror Filter Banks Using Digital All-Pass Lattice Filters

Authors: Ju-Hong Lee, Chong-Jia Ciou


This paper deals with the problem of two-dimensional (2-D) recursive two-channel quincunx quadrature mirror filter (QQMF) banks design. The analysis and synthesis filters of the 2-D recursive QQMF bank are composed of 2-D recursive digital allpass lattice filters (DALFs) with symmetric half-plane (SHP) support regions. Using the 2-D doubly complementary half-band (DC-HB) property possessed by the analysis and synthesis filters, we facilitate the design of the proposed QQMF bank. For finding the coefficients of the 2-D recursive SHP DALFs, we present a structure of 2-D recursive digital allpass filters by using 2-D SHP recursive digital all-pass lattice filters (DALFs). The novelty of using 2-D SHP recursive DALFs to construct a 2-D recursive QQMF bank is that the resulting 2-D recursive QQMF bank provides better performance than the existing 2-D recursive QQMF banks. Simulation results are also presented for illustration and comparison.

Keywords: All-pass digital filter, doubly complementary, lattice structure, symmetric half-plane digital filter, quincunx QMF bank.

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[1] S. I. Park, M. J. Smith, and R. M. Mersereau, “Improved structure of maximally decimated directional filter banks for spatial image analysis”, IEEE Transactions on Image Processing, vol. 13, no. 11, pp. 1424-1431, Nov. 2004.
[2] T. T. Nguyen and S. P. Oraintara, “Multiresolution direction filter banks: Theory, design and application”, IEEE Transactions on Signal Processing, vol. 53, no. 10, pp. 3895-3905, Oct. 2005.
[3] Z. Lei and A. P. Makur, “Two-dimensional antisymmetric linear phase filter bank construction using symmetric completion”, IEEE Transactions on Circuits and Systems-II: Express Briefs, vol. 54, no. 1, pp. 57 –60, Jan. 2007.
[4] P. G. Patwardhan, B. Patil, and V. M. Gadre, “Polyphase conditions and structures for 2-D quincunx FIR filter banks having quadrantal or diagonal symmetries” IEEE Transactions on Circuits and Systems-II: Express Briefs, vol. 54, no. 9, pp. 790 –794, Sept. 2007.
[5] J.-H. Lee and Y.-H. Yang, “Two-dimensional recursive digital filters with nearly circular-symmetric magnitude response and approximately linear phase,” International Journal of Circuit Theory and Applications, vol. 39, no. 12, pp. 1215-1229, Dec. 2011.
[6] J.-H. Lee and Y.-H. Yang, “Two-channel quincunx QMF banks using two-dimensional digital allpass filters,” IEEE Transactions on Circuits and Systems – I, vol. 56, no. 12, pp. 2644-2654, Dec. 2009.
[7] M. Vetterli and G. Karlsson, “Theory of two-dimensional multirate filter banks,” IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 38, no. 6, pp. 925-937, June 1990.
[8] P. Siohan, “2-D FIR filter design for sampling structure conversion,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 1, no. 4, pp. 337-350, Apr. 1991.
[9] A. Knoll, “Filter design for the interpolation of highly subsampled pictures,” Signal Processing: Image Communication, vol. 3, pp. 239-248, 1991.
[10] 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.
[11] S. C. Pei and J.-J. Shyu, “Eigenfilter design of 1-D and 2-D IIR digital all-pass filters,” IEEE Transactions on Signal Processing, vol. 42, no. 4, pp. 966-968, Apr. 1994.
[12] J. Nocedal and S. J. Wright, Numerical Optimization, New York: Springer-Verlag, 1999.
[13] Vaidyanathan P. P. Multirate Systems and Filter Banks. New Jersey, Prentice Hall: Englewood Cliffs, 1992.