Circuits, Systems, and Signal Processing

, Volume 38, Issue 7, pp 3356–3369 | Cite as

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

  • Tahar BensouiciEmail author
  • Abdelfatah Charef
  • Assadi Imen
Short Paper


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 zm\( (m \in \Re^{ + } ) \). 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.


Fractional delay FIR filters Binomial series expansion Discrete fractional system Broader bandwidth 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Tahar Bensouici
    • 1
    Email author
  • Abdelfatah Charef
    • 2
  • Assadi Imen
    • 2
  1. 1.Département de Télécommunication, Faculté d’Electronique et InformatiqueUniversité USTHBBab-EzzouarAlgeria
  2. 2.Laboratoire de Traitement du Signal Département d’ElectroniqueUniversité des Frères Mentouri Constantine Route Ain El-beyConstantineAlgeria

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