Circuits, Systems, and Signal Processing https://doi.org/10.1007/s00034-018-1000-8 SHORT PAPER A Simple Design of Fractional Delay FIR Filter Based on Binomial Series Expansion Theory Tahar Bensouici 1 · Abdelfatah Charef 2 · Assadi Imen 2 Received: 11 January 2018 / Revised: 23 November 2018 / Accepted: 24 November 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 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 ∈ℜ + ). 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. Keywords Fractional delay FIR filters · Binomial series expansion · Discrete fractional system · Broader bandwidth 1 Introduction In recent years, fractional order signal processing has received considerable inter- est in many engineering applications including the implementations of the fractional delay/forward filters, the fractional integrators/differentiators, the fractional Fourier transform and the fractional wavelet transform [1, 4, 5, 15, 18]. B Tahar Bensouici h.bensouici@gmail.com Abdelfatah Charef afcharef@yahoo.com Assadi Imen assadi.imen@gmail.com 1 Département de Télécommunication, Faculté d’Electronique et Informatique, Université USTHB, BP. 32, 16111 Bab-Ezzouar, Algeria 2 Laboratoire de Traitement du Signal Département d’Electronique, Université des Frères Mentouri Constantine Route Ain El-bey, 25000 Constantine, Algeria