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A Simple Design of Fractional Delay FIR Filter Based on Binomial Series Expansion Theory

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Abstract

Fractional delay filters modeling non-integer delays are digital filters that ideally have flat group delays. This paper proposes a simple design method of fractional delay FIR filter based on binomial series expansion theory. First, the design technique is based on the binomial series expansion method which is applied to a discrete fractional system to obtain a closed form FIR digital filter which approximates the digital fractional delay operator z−m\( (m \in \Re^{ + } ) \). Then, the principal differentiation is used to design fractional delay FIR filter with a broader group delay bandwidth. Finally, numerical examples of fractional delay FIR filter design show that the proposed approach yields better performance compared to the existing techniques.

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Authors and Affiliations

  1. Département de Télécommunication, Faculté d’Electronique et Informatique, Université USTHB, BP. 32, 16111, Bab-Ezzouar, Algeria

    Tahar Bensouici

  2. Laboratoire de Traitement du Signal Département d’Electronique, Université des Frères Mentouri Constantine Route Ain El-bey, 25000, Constantine, Algeria

    Abdelfatah Charef & Assadi Imen

Authors
  1. Tahar Bensouici
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  2. Abdelfatah Charef
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  3. Assadi Imen
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Correspondence to Tahar Bensouici.

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Bensouici, T., Charef, A. & Imen, A. A Simple Design of Fractional Delay FIR Filter Based on Binomial Series Expansion Theory. Circuits Syst Signal Process 38, 3356–3369 (2019). https://doi.org/10.1007/s00034-018-1000-8

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