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Design of Nonrecursive Digital Filters Using the Ultraspherical Window Function

Abstract

An efficient method for the design of nonrecursive digital filters using the ultraspherical window function is proposed. Economies in computation are achieved in two ways. First, through an efficient formulation of the window coefficients, the amount of computation required is reduced to a small fraction of that required by standard methods. Second, the filter length and the independent window parameters that would be required to achieve prescribed specifications in lowpass, highpass, bandpass, and bandstop filters as well as in digital differentiators and Hilbert transformers are efficiently determined through empirical formulas. Experimental results demonstrate that in many cases the ultraspherical window yields a lower-order filter relative to designs obtained using windows like the Kaiser, Dolph-Chebyshev, and Saramäki windows. Alternatively, for a fixed filter length, the ultraspherical window yields reduced passband ripple and increased stopband attenuation relative to those produced when using the alternative windows.

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Correspondence to Stuart W. A. Bergen.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Bergen, S.W.A., Antoniou, A. Design of Nonrecursive Digital Filters Using the Ultraspherical Window Function. EURASIP J. Adv. Signal Process. 2005, 406531 (2005). https://doi.org/10.1155/ASP.2005.1910

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Keywords and phrases

  • nonrecursive digital filters
  • FIR filters
  • window functions
  • ultraspherical window
  • digital differentiators
  • Hilbert transformers