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Design of smallest size two-dimensional linear-phase FIR filters with magnitude error constraint

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Abstract

This paper presents an online procedure that produces the smallest feasible size of two-dimensional FIR filters with prescribed magnitude error constraint. The procedure uses the mean square normalized error of constrained and unconstrained least-square filters to produce the initial and the subsequent sizes that converge to the smallest feasible one in a few iterations, where the constrained least-square filters are defined as the least-square filters satisfying the magnitude error constraint. The procedure finally returns a smallest size filter that satisfies the magnitude error constraint and has least total squared magnitude error. Design examples of diamond-shaped, rectangular, and elliptic filters are provided, and comparisons with an exhaustive search are given.

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References

  • Adams J.W., Sullivan J. (1998). Peak-Constrained Least-Squares Optimization. IEEE Transactions on Signal Processing 46(2): 306–321

    Article  Google Scholar 

  • Ahmad M.O., Wang J.-D. (1989). An analytical least square solution to the design problem of two-dimensional FIR filters with quadrantally symmetric and antisymmetric frequency response. IEEE Transactions Circuits and Systems 36(7): 968–979

    Article  Google Scholar 

  • Algazi V.R., Suk M., Rim C.K. (1986) Design of almost minimax FIR filters in one and two dimensions by WLS techniques. IEEE Transactions Circuits and Systems 33(6): 590–596

    Article  Google Scholar 

  • Boyd S., Vandenberghe L. (2004). Convex Optimization. Cambridge, Cambridge University Press

    MATH  Google Scholar 

  • Gill, P. E., Murray, W., & Wright, M. H. (1991). Numerical Linear Algebra and Optimization, Vol. 1, Redwood City, CA: Addison-Wesley.

  • Gislason E., Johansen M., Conradsen K., Erboll B.K., Jacobsen S.K. (1993). Three different criteria for the design of two-dimensional zero phase FIR digital filters. IEEE Transactions Signal Processing 41(10): 3070–3074

    Article  MATH  Google Scholar 

  • Goldfarb D., Idnani A. (1983). A numerically stable dual method for solving strictly convex quadratic programs. Mathematical Programming 27: 1–33

    Article  MATH  MathSciNet  Google Scholar 

  • Hsieh C.H., Kuo C.M., Jou Y.D., Han Y.L. (1997). Design of Two-dimensional FIR digital filters by a two-dimensional WLS technique. IEEE Transactions on Circuits and Systems II 44(5): 348–356

    Article  Google Scholar 

  • Lai X.P. (2005). Projected Least-Squares Algorithms for Constrained FIR Filter Design. IEEE Transactions Circuits and Systems - I 52(11): 2436–2443

    Article  Google Scholar 

  • Lai X.P. (2006). A PLS algorithm for design of linear-phase 2-D FIR filter with prescribed magnitude ripples. Proceedings IEEE International Conference on Communication, Circuits and Systems 1: 196–200

    Article  Google Scholar 

  • Lang M., Selesnick I.W., Burrus C.S. (1996). Constrained least squares design of 2-D FIR filters. IEEE Transactions Signal Processing 44(5): 1234–1241

    Article  Google Scholar 

  • Parks T.W., McClellan J.H. (1972). Chebyshev approximation for nonrecursive dgital filters with linear phase. IEEE Transactions on Circuit Theory 19(3): 189–194

    Article  Google Scholar 

  • Rabiner L.R., Gold B. (1975). Theory and Applications of Digital Signal Processing. Englewood Cliffs, NJ, Prentice-Hall

    Google Scholar 

  • Sunder S., Ramachandran R.P. (1994). An efficient least-squares approach for the design of two-dimensional linear-phase nonrecursive filters. Proceedings IEEE International Symposium Circuits and Systems 2: 577–580

    Google Scholar 

  • Wright S.J. (1997). Primal-Dual Interior Point Methods. Philadelaphia, PA, SIAM

    MATH  Google Scholar 

  • Zhu W.P., Ahmad M.O., Swamy M.N.S. (1994). An analytical approach for obtaining a closed-form solution to the least-square design problem of 2-D zero-phase FIR filters. IEEE Transactions Circuits and Systems - II 41(12): 796–807

    Google Scholar 

  • Zhu W.P., Ahmad M.O., Swamy M.N.S. (1999). A Least-Square Design Approach for 2-D FIR Filters with Arbitrary Frequency Response. IEEE Transactions on Circuits and Systems – II 46(8): 1027–1034

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Information Engineering, Shandong University at Weihai, Weihai, 264209, People’s Republic of China

    Xiaoping Lai

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  1. Xiaoping Lai
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Correspondence to Xiaoping Lai.

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Lai, X. Design of smallest size two-dimensional linear-phase FIR filters with magnitude error constraint. Multidim Syst Sign Process 18, 341–349 (2007). https://doi.org/10.1007/s11045-006-0007-7

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  • DOI: https://doi.org/10.1007/s11045-006-0007-7

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