2-D lossless FIR filter design using synthesis of the paraunitary transfer function matrix

• Autorzy: Wawryn Krzysztof , Poczekajło Paweł

Identyfikatory

DOI

10.34768/amcs-2023-0048

• Języki publikacji: EN

Abstrakty

EN

A synthesis method for designing two-dimensional lossless finite impulse response (FIR) filters for various digital signal processing tasks is proposed. The synthesis method is based on using a 2-D embedding approach to obtain the paraunitary transfer function matrix of the lossless FIR filter. The elements of the paraunitary transfer function matrix are the transfer function of a given lossy FIR structure and the transfer functions for its complementary structures. The embedding method is used to design complementary FIR filter structures for several known lossy FIR filters. The lossless FIR filter matrix obtained in this article has a size of 3 × 1 and satisfies the paraunitary conditions. The conditions are described by a set of nonlinear equations. A modified Newton method is used to solve this set of equations. The proposed design method is used to determine the lossless structures of two-dimensional FIR filters for various digital processing tasks.

Słowa kluczowe

EN

lossless system; paraunitary transfer function matrix; FIR filter; embedding method

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2023
• Tom: Vol. 33, no. 4
• Strony: 673--686
• Opis fizyczny: Bibliogr. 40 poz., rys.

Twórcy

autor

Wawryn Krzysztof

• Department of Digital Signal Processing Systems, Koszalin University of Technology, ul. Śniadeckich 2, 75-453 Koszalin, Poland

autor

Poczekajło Paweł

• Department of Digital Signal Processing Systems, Koszalin University of Technology, ul. Śniadeckich 2, 75-453 Koszalin, Poland

Bibliografia

• [1] Andraka, R. (1998). A survey of CORDIC algorithms for FPGA based computers, Symposium on Field Programmable Gate Arrays, North Kingstown, USA, pp. 191-200.
• [2] Anju, R.T. and Mathurakani, M. (2016). Realization of hardware architectures for Householder transformation based QR decomposition using Xilinx system generator block sets, International Journal of Science Technology and Engineering 2(8): 202-206.
• [3] Antoniou, A. (2005). Digital Signal Processing: Signals, Systems, and Filters, McGraw-Hill Education, New York.
• [4] Basu, S. and Fettweis, A. (1985). On the factorization of scattering transfer matrices of multidimensional lossless two-ports, IEEE Transactions on Circuits and Systems 32(9): 925-934.
• [5] Belevitch, V. (1968). Classical Network Theory, Holden-Day, San Francisco.
• [6] Bose, N.K. and Strintzis, M.G. (1973). A solution to the multivariable matrix factorization problem, Journal of Engineering Mathematics 7: 263-271.
• [7] Brent, R.P. and Zimmermann, P. (2010). Modern Computer Arithmetic, Cambridge University Press, Cambridge.
• [8] Brugière, T., Baboulin, M., Valiron, B. and Allouche, C. (2019). Quantum circuits synthesis using Householder transformations, Computer Physics Communications 248: 107001.
• [9] Charalambous, C. (1985). The performance of an algorithm for minimax design of two-dimensional linear phase FIR digital filters, IEEE Transactions on Circuits and Systems 32(10): 1016-1028.
• [10] Cormen, T.H., Leiserson, C.E., Rivest, R.L. and Stein, C. (2009). Introduction to Algorithms, 3rd Edition, MIT Press, Cambridge.
• [11] Deprettere, E. and Dewilde, P. (1980). Orthogonal cascade realization of real multiport digital filters, International Journal of Circuit Theory and Applications 8(3): 245-272.
• [12] Dewilde, P. (2019). The power of orthogonal filtering, IEEE Circuits and Systems Magazine 18: 70-C3.
• [13] Fettweis, A. (1971). Digital filter structures related to classical filter networks, Archiv der elektrischen Übertragung: AEÜ 25: 79-89.
• [14] Fettweis, A. (1982). On the scattering matrix and the scattering transfer matrix of multidimensional lossless two-ports, Archiv der elektrischen Übertragung: AEÜ 36: 374-381.
• [15] Fettweis, A. (1991). The role of passivity and losslessness in multidimensional digital signal processing-New challenges, IEEE International Symposium on Circuits and Systems, Singapore, Vol. 1, pp. 112-115.
• [16] Golub, G. and Loan, C. (1996). Matrix Computations, Johns Hopkins University Press, Baltimore.
• [17] Kaczorek, T. (2008). The choice of the forms of Lyapunov functions for a positive 2D Roesser model, International Journal of Applied Mathematics and Computer Science 17(4): 471-475, DOI: 10.2478/v10006-007-0039-7.
• [18] Kaczorek, T. and Rogowski, K. (2010). Positivity and stabilization of fractional 2D linear systems described by the Roesser model, International Journal of Applied Mathematics and Computer Science 20(1): 85-92, DOI: 10.2478/v10006-010-0006-6.
• [19] Liu, Q., Ling, B., Dai, Q., Miao, Q. and Liu, C. (2017). Optimal maximally decimated M-channel mirrored paraunitary linear phase FIR filter bank design via norm relaxed sequential quadratic programming, Journal of Industrial and Management Optimization 13(4): 1993-2011.
• [20] Lu, W.-S. (2002). A unified approach for the design of 2-D digital filters via semidefinite programming, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 49(6): 814-826.
• [21] Lu, W.-S. and Antoniou, A. (1992). Two-Dimensional Digital Filters, 1st Edition, CRC Press, New York.
• [22] Luenbergerand, D.G. and Ye, Y. (2008). Linear and Nonlinear Programming, Kluwer Academic Publishers, Stanford.
• [23] Mitra, S.K. and Kaiser, J.K. (1993). Handbook of Digital Signal Processing, Wiley-Interscience, New York.
• [24] Piekarski, M. and Wirski, R. (2005). On the transfer matrix synthesis of two-dimensional orthogonal systems, Proceedings of the 2005 European Conference on Circuit Theory and Design, Cork, Ireland, Vol. 3, pp. III/117–III/120.
• [25] Puchala, D. (2022). Effective lattice structures for separable two-dimensional orthogonal wavelet transforms, Bulletin of the Polish Academy of Sciences: Technical Sciences 70(3): 1-8.
• [26] Rao, C. and Dewilde, P. (1987). On lossless transfer functions and orthogonal realizations, IEEE Transactions on Circuits and Systems 34(6): 677-678.
• [27] Roesser, R. (1975). A discrete state-space model for linear image processing, IEEE Transactions on Automatic Control 20(1): 1-10.
• [28] Sienkowski, S. and Krajewski, M. (2021). On the statistical analysis of the harmonic signal autocorrelation function, International Journal of Applied Mathematics and Computer Science 31(4): 729-744, DOI: 10.34768/amcs-2021-0050.
• [29] Smith III, J.O. (2007). Introduction to Digital Filters with Audio Applications, W3K Publishing, Stanford.
• [30] Soman, A. and Vaidyanathan, P. (1995). A complete factorization of paraunitary matrices with pairwise mirror-image symmetry in the frequency domain, IEEE Transactions on Signal Processing 43(4): 1002-1004.
• [31] Stancic, S., Rajovic, V. and Slijepcevic, I. (2018). Performance of FPGA implementation of the orthogonal two-channel filter bank for perfect reconstruction, 26th Telecommunications Forum, TELFOR 2018, Belgrade, Serbia, pp. 1-4.
• [32] Vaidyanathan, P. and Mitra, S. (2019). Robust digital filter structures: A direct approach, IEEE Circuits and Systems Magazine 19(1): 14-32.
• [33] Valkova-Jarvis, Z., Stoynov, V. and Mihaylova, D. (2019). Designing efficient bilinear bicomplex orthogonal digital filters, IEEE Conference on Microwave Theory and Techniques in Wireless Communications, MTTW 2019, Riga, Latvia, pp. 5-8.
• [34] Wang, J., Chen, Y., Chakraborty, R. and Yu, S. (2020). Orthogonal convolutional neural networks, IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020, Seattle, USA, pp. 11502-11512.
• [35] Wawryn, K. and Wirski, R. (2009). Synthesis of 2-D lossless FIR filter transfer function matrix, 2009 7th International Conference on Information, Communications and Signal Processing, ICICS 2009, Macau, China, pp. 1-5.
• [36] Wawryn, K., Wirski, R. and Strzeszewski, B. (2010). Implementation of finite impulse response systems using rotation structures, International Symposium on Information Theory and Its Applications, ISITA 2010, Taichung, Taiwan, pp. 606-610.
• [37] Wirski, R. (2008). On the realization of 2-D orthogonal state-space systems, Signal Processing 88(11): 2747-2753.
• [38] Wirski, R. and Wawryn, K. (2008). Roesser’s model realization of 2-D FIR lossless transfer matrices, 2008 International Symposium on Information Theory and Its Applications, Auckland, New Zealand, pp. 1-6.
• [39] Wnuk, M. (2008). Remarks on hardware implementation of image processing algorithms, International Journal of Applied Mathematics and Computer Science 18(1): 105-110, DOI: 10.2478/v10006-008-0010-2.
• [40] Yang, Y., Zhu, W.-P. and Yan, J. (2017). Minimax design of orthogonal filter banks with sparse coefficients, 30th IEEE Canadian Conference on Electrical and Computer Engineering, CCECE 2017, Windsor, Canada, pp. 1-4.