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Abstract

The inverse ultraspherical filter is derived and its properties analyzed. It is shown that the inverse ultraspherical filter has smaller transition band than the inverse Chebyshev filter under certain circumstances while still maintaining the maximally flat passband characteristic. Filter pole and zero calculations are described and typical magnitude and delay responses generated. Nomographs of inverse ultraspherical filters are also provided for determining filter order and for possible magnitude response optimization.

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References

  1. B.J. Bennett, “A new filter synthesis technique—The hourglass.” IEEE Trans. Circuits and Systems, vol. 35, pp. 1469–1477.

  2. D.R. Huard, J. Andersen, and R.G. Hove, “Linear phase analog filter design with arbitrary stopband zeros.” Int. Symp. Circuits and Systems, vol. 2, pp. 839–842, 1992.

    Google Scholar 

  3. L. Weinberg, Network Analysis and Synthesis. McGraw-Hill, New York, 1962.

    Google Scholar 

  4. C.S. Lindquist, Active Network Design with Signal Filtering Applications. Long Beach, CA, Steward & Sons, 1977.

    Google Scholar 

  5. H.K. Kim, S.S. Song, and D.Y. Kim, “Some prominent aspects of the inverse Chebyshev functions.” IEEE Trans. Circuits and Systems, vol. 38, pp. 320–322, March 1991.

    Article  Google Scholar 

  6. J.-C. Ahn, S.-W. Choi, C.-H. Yun, and D.-Y. Kim, “Some prominent characteristics of the modified inverse Chebyshev function.” Proc. 40th Midwest Symp. Circuits and Systems, vol. 1, pp. 328–333, 1998.

    Google Scholar 

  7. D. Baez-Lopez and E. Jimenez-Lopez, “A modified inverse Chebyshev filter with an all positive elements ladder passive realization.” Proc. Int. Symp. Circuits and Systems, vol. 6, pp. 49–52, 1999.

    Google Scholar 

  8. M. Lutovac and D. Rabrenović, “Improved version of the inverse Chebyshev filter.” Electron. Lett., vol. 26, pp. 1256–1257, 1990.

    Google Scholar 

  9. M. Vlcek and R. Unbehauen, “Zolotarev polynomials and optimal FIR filters.” IEEE Trans. Sig. Proc., vol. 47, pp. 717–730, March, 1999.

    Google Scholar 

  10. K. Hájek and J. Sedlácek, “A new TICFU transitional approximation.” Proc. ECCTD Istanbul, vol. 1, pp. 913–916, 1995.

    Google Scholar 

  11. D.E. Johnson and J.R. Johnson, “Low-pass filters using ultraspherical polynomials.” IEEE Trans. Circuit Theory, vol. CT-13, pp. 364–369, Dec. 1966.

    Google Scholar 

  12. A. Saèd, J.J. Soltis, and M. Ahmadi, “Gegenbauer (ultraspherical) polynomials for Gabor-type wavelet approximation and FIR filter function generation in wavelet analysis.” Canadian Conf. on Electrical and Computer Engineering, vol. 2, pp. 878–881, 1995.

    Google Scholar 

  13. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products. Academic Press, New York, 1980.

    Google Scholar 

  14. J.N. Hallberg and C.S. Lindquist, “Nomographs and filters.” J. Franklin Inst., vol. 302, pp. 111–145, Aug. 1976.

    Google Scholar 

  15. C.A. Corral, C.S. Lindquist, and P.B. Aronhime, “Sensitivities of band-edge selectivities.” J. Analog Integrated Circuits and Sig. Proc., vol. 19, pp. 189–196, May 1999.

    Google Scholar 

  16. R. V. Churchill, Complex Variables and Applications, 2nd edition, McGraw-Hill, New York, 1960.

    Google Scholar 

  17. J. Vlach, Computerized Approximation and Synthesis of Linear Networks, Wiley, New York, 1969.

    Google Scholar 

  18. D.M. Petrela and A. Budak, “Pole locations for ultraspherical filters.” IEEE Trans. Circuit Theory, vol. CT-17, pp. 668–670, Nov. 1970.

    Google Scholar 

  19. K.W. Henderson and W.H. Kautz, “Transient responses of conventional filters.” IRE Trans. Circuit Theory, vol. CT-5, pp. 333–347, Dec. 1958.

    Google Scholar 

  20. C.S. Lindquist and C.A. Corral, “Selectivity nomographs for classical filters.” J. Franklin Inst., vol. 339, pp. 61–76, April 2002.

    Google Scholar 

  21. C.A. Corral and C.S. Lindquist, “Design for optimum classical filters.” IEE Proc. Circuits, Devices, and Systems, vol. 149, pp. 291–300, Oct./Dec. 2002.

    Google Scholar 

  22. C.A. Corral, “Nomographs and classical filter sensitivity optimization.” IEEE Int. Symp. Circuits Syst., vol. 1, pp. 541–544, 2002.

    Google Scholar 

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Celestino A. Corral was born in Havana, Cuba. He earned his Bachelor’s, Master’s and Ph.D. degrees in electrical engineering from the University of Miami, Florida, in 1985, 1987, and 1993, respectively. He completed his Ph.D. program under a Patricia Roberts Harris fellowship. From 1988 to 1990 Dr. Corral was a Member of the Technical Staff at Sandia National Laboratories, Albuquerque, New Mexico, where he was involved in the analysis, modeling, and design of custom circuits for piezoelectric sensor components. In 1994, he joined Scientific-Atlanta in Atlanta, Georgia, as an Associate Staff RF Engineer and worked on communication systems and specialized microwave software. In 1997 he was Senior Design Engineer at Origin Data Systems in Boca Raton, Florida, where he had multiple roles in system, hardware, and software development for a novel asset management/RFID system. Currently, Dr. Corral is a Distinguished Member of the Technical Staff in Motorola Labs, Plantation, Florida, and is involved in ultra-wideband, wideband, and propagation research. His interests include circuit and filter theory, communication systems, numerical analysis, signal processing, and constrained optimization. He has published over twenty-five journal and conference papers, has six patents filed, and two trade secrets.

Dr. Corral was principal recipient of the Myril B. Reed Best Paper Award for the 40th Midwest Symposium on Circuits and Systems in 1997. Dr. Corral is also the principal recipient of the Ambrose Fleming Premium for IEE Proceedings on Circuits, Devices, and Systems, 2000. Dr. Corral is a Senior Member of IEEE and a member of Omicron Delta Kappa, Tau Beta Pi, and Eta Kappa Nu honor societies.

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Corral, C.A. Inverse Ultraspherical Filters. Analog Integr Circ Sig Process 42, 147–159 (2005). https://doi.org/10.1007/s10470-005-5750-4

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  • DOI: https://doi.org/10.1007/s10470-005-5750-4

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