A Simple Method for Designing 2D |M|-Channel Near-PR Filter Banks with Linear Phase Property
Two dimensional (2D) nonseparable filter banks with linear phase (LP) are desired for image sub-band coding and compression. In this paper, we propose a method for designing 2D nonseparable filter banks with the LP and near perfect reconstruction (near-PR) properties. By combining the unimodular transformation and a separable |M|-channel LP filter bank, the design problem is simplified to that of two one-dimensional (1D) LP filter banks. For 1D case, a novel method by employing partial cosine modulation is used to design near-PR filter banks with LP analysis and synthesis filters. For 2D case, we cascade two 1D near-PR LP filter banks in the form of tree structure to design a separable LP filter bank. With the unimodular transformation, a nonseparable LP filter bank is obtained. In addition, the filter bank achieves the near-PR property without sophisticated nonlinear optimization procedures. Design example shows the efficiency and simplicity of the proposed method.
KeywordsFilter Bank Perfect Reconstruction Analysis Filter Prototype Filter Synthesis Filter
Unable to display preview. Download preview PDF.
- 4.Viscito, E., Allebach, J.P.: The analysis and design of multidimensional FIR perfect reconstruction filter banks for arbitrary sampling lattices. IEEE Trans. CAS 38(1), 29–42 (1991)Google Scholar
- 5.Nguyen, T.T., Oraintara, S.: Multidimensional filter banks design by direct optimization. IEEE ISCAS 2, 1090–1093 (2005)Google Scholar
- 6.Lin, Y.P., Vaidyanathan, P.P.: Two-dimensional paraunitary cosine modulated perfect reconstruction filter banks. IEEE ISCAS 1, 752–755 (1995)Google Scholar
- 7.Ikehara, M.: Cosine-modulated 2 dimensional FIR filter banks satisfying perfect reconstruction. IEEE ICASSP 3, 137–140 (1994)Google Scholar
- 8.Lin, Y.P., Vaidyanathan, P.P.: Two-dimensional linear phase cosine modulated filter banks. IEEE ISCAS 2, 73–76 (1996)Google Scholar
- 9.Nagai, T., Ikehara, M.: Cosine modulated 2-dimensional perfect reconstruction FIR filter banks with linear phase. IEEE ICASSP 3, 1483–1486 (1996)Google Scholar
- 10.Vaidyanathan, P.P.: The role of Smith-form decomposition of integer-matrices, in multidimensional multirate systems. IEEE ICASSP 3, 1777–1780 (1991)Google Scholar
- 11.Vaidyanathan, P.P.: New results in multidimensional multirate systems. IEEE ISCAS 1, 468–471 (1991)Google Scholar
- 14.Vaidyanathan, P.P.: Multirate Systems and Filter Banks. Prentice Hall, Englewood Cliffs (1992)Google Scholar
- 15.Xie, X.M., Shi, G.M., Chen, X.Y.: Optimal prototype filters for near-perfect-reconstruction cosine-modulated filter banks. In: Hao, Y., Liu, J., Wang, Y.-P., Cheung, Y.-m., Yin, H., Jiao, L., Ma, J., Jiao, Y.-C. (eds.) CIS 2005. LNCS (LNAI), vol. 3802, pp. 851–856. Springer, Heidelberg (2005)CrossRefGoogle Scholar