Circuits, Systems, and Signal Processing

, Volume 37, Issue 5, pp 2001–2020 | Cite as

Chained-Function Filter Synthesis Based on the Legendre Polynomials

  • Nikola Stojanović
  • Negovan Stamenković
  • Ivan Krstić


A new kind of filter called Legendre chained-function (LCF) filter with characteristic function given by the product of low-degree Legendre orthogonal polynomials (seed functions) is studied in this paper. LCF filter magnitude response exhibits unequal ripple level in the passband compared to Chebyshev chained-function filter with identical edge ripple factor at the passband edge. A proper combination of seed functions, i.e., a product of them, is used to control the maximum ripple in the passband, which affects the return loss, selectivity and a group delay characteristics of a filter. By selecting one of the possible combinations of seed functions (thus obtaining various degrees of freedom in filter design), filters with improved performances compared to traditional approximation techniques can be obtained. The degrees of freedom increase if the degree of filter increases. Compared to existing Chebyshev chained-function (CCF) filters, whose performances are also presented, and Butterworth function filters as a special case of both LCF and CCF filters, the new family of LCF filters has many advantages. A table summarizing properties of CCF and LCF filters is given for design purpose.


Chained-function filter Legendre polynomial Chebyshev polynomial Magnitude response Group delay characteristic Monte Carlo simulation 



The authors wish to thank Professor V. S. Stojanović of the University of Niš, Niš, Serbia for his valuable comments and suggestions. The work presented here was partly supported by the Serbian Ministry of Education and Science in the frame of the Projects TR 32009.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Faculty of Electronic EngineeringUniversity of NišNišSerbia
  2. 2.Faculty of Natural Science and MathematicsUniversity of PrištinaKosovska MitrovicaSerbia
  3. 3.Faculty of Technical ScienceUniversity of PrištinaKosovska MitrovicaSerbia

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