Analysis of Novel Window Based on the Polynomial Functions

  • Mahdi Nouri
  • Sajjad Abazari Aghdam
  • Somayeh Abazari Aghdam
Part of the Communications in Computer and Information Science book series (CCIS, volume 250)


A simple form of a window function with application to FIR filter design is implemented two parts, that is using polynomial functions with grade two and three and computational complexity becomes unavoidable. The spectral characteristic of proposed window is studied in details, and its performance is compared with traditional windows such as Kaiser Window. This is performed in ripple ratio and sidelobe roll-off ratio for the same window length and normalized mainlobe width. Simulation results show that proposed window presents better ripple ratio for the both narrower and wider mainlobe width and larger sidelobe roll-off ratio, The new window is almost quasi equi-ripple. The other advantages for our window are ability to use in various applications by changing two parameters this window can change it’s time frame and spectrum and want smaller window length compared with other windows.


window functions Filter Complexity Spectral efficiency Ripple Ratio 


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  1. 1.
    Antoniou, A.: Digital signal processing: Signal, systems, and filters. McGraw-Hill (2005)Google Scholar
  2. 2.
    Kaiser, J.F., Schafer, R.W.: On the use of the Io-sinh window for spectrum analysis. IEEE Trans. Acoustics, Speech, and Signal Processing 28(1), 105–107 (1980)CrossRefGoogle Scholar
  3. 3.
    Kaiser, J.F.: Nonrecursive digital filter design using I0-sinh window function. In: Proc. IEEE Int. Symp. Circuits and Systems (ISCAS 1974), San Francisco, Calif., USA, pp. 20–23 (April 1974)Google Scholar
  4. 4.
    Dolph, C.L.: A Current Distribution for Broadside Arrays Which Optimizes the Relationship Between Beamwidth and Side-lobe Level. In: Proc. IRE, vol. 34, pp. 335–348 (June 1946)Google Scholar
  5. 5.
    Saramaki, T.: A class of window functions with nearly minimum sidelobe energy for designing FIR filters. In: Proc. IEEE Int. Symp. Circuits and Systems (ISCAS 1989), Portland, Ore., USA, vol. 1, pp. 359–362 (1989)Google Scholar
  6. 6.
    Bergen, S.W.A., Antoniou, A.: Design of Ultraspherical window functions with prescribed spectral characteristics. EURASIP Journal on Applied Signal Processing (13), 2053–2065 (2004)Google Scholar
  7. 7.
    Oppenheim, A., Schafer, R., Buck, J.: Discrete-Time Signal Processing, 2nd edn. Prentice-Hall (1999)Google Scholar
  8. 8.
    Proakis, J., Manolakis, D.G.: Digital Signal Processing, 4th edn. Prentice-Hall (2007)Google Scholar
  9. 9.
    Antoniou, A.: Digital Filters. McGraw-Hill Inc., N.Y (1993)Google Scholar
  10. 10.
    Tukey, J.W.: An introduction to the calculations of numerical spectrum analysis. Spectral Analysis of Time Series, 25–46 (1967)Google Scholar
  11. 11.
    Deczky, A.G.: Unispherical windows. In: Proceedings IEEE ISCS, vol. II, pp. 85–89 (2001)Google Scholar
  12. 12.
    Jascula, M.: New windows family based on modified Legendre polynomials. In: Proceedings IEEE IMTC, pp. 553–556 (2002)Google Scholar
  13. 13.
    Zierhofer, C.M.: Data window with tunable side lobe ripple decay. IEEE Signal Processing Letters 14(11) (November 2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Mahdi Nouri
    • 1
  • Sajjad Abazari Aghdam
    • 2
  • Somayeh Abazari Aghdam
    • 3
  1. 1.Department of Electrical EngineeringUniversity of Science & TechnologyIran
  2. 2.Department of Electrical EngineeringIslamic Azad South Tehran UniversityTehranIran
  3. 3.Department of Electrical EngineeringIslamic Azad UniversityMahabadIran

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