Int. J. Reasoning-based Intelligent Systems, Vol. 5, No. 1, 2013 3 Copyright © 2013 Inderscience Enterprises Ltd. Design of first-order differentiator utilising FIR and IIR sub-filters Ljiljana D. Milić* Faculty of Electrical Engineering, University of Belgrade, Belgrade, Serbia Email: milic@kondor.imp.bg.ac.rs *Corresponding author Miroslav D. Lutovac Faculty of Business, Singidunum University, Belgrade, Serbia Email: mlutovac@singidunum.ac.rs Jelena D. Ćertić Telecommunications Department, Faculty of Electrical Engineering, University of Belgrade, Belgrade, Serbia Email: certic@etf.rs Abstract: In this paper, we propose a novel approach for constructing the first-order differentiator. It has been shown recently that an efficient Finite Impulse Response (FIR) wideband differentiator can be synthesised when applying the multirate and Frequency-Response Masking (FRM) techniques. The overall signal processing task is shared between a very low- order differentiator and an FIR half-band filter. The novelty of this paper is the usage of an approximately linear-phase IIR half-band filter based on the parallel connection of all-pass sub- filter and pure delay. The structure of resulting wideband differentiator consists of the approximately linear phase all-pass sub-filter, two low-order FIR polyphase sub-filters, and the delay element. The knowledge-based design has been used for the analysis and improvements of the wideband differentiator. The proposed system provides computational savings and exhibits a significantly smaller overall delay if compared with the corresponding solution based on FIR filters only. Keywords: all-pass filter; approximately linear phase IIR filter; differentiator; half-band filter; multirate filtering. Reference to this paper should be made as follows: Milić, L.D., Lutovac, M.D. and Ćertić, J.D. (2013) ‘Design of first-order differentiator utilising FIR and IIR sub-filters’, Int. J. Reasoning- based Intelligent Systems, Vol. 5, No. 1, pp.3–11. Biographical notes: Ljiljana D. Milić received the Dipl.-Eng., MSc and DSc degrees from the University of Belgrade in 1962, 1973 and 1978, respectively, all in Electrical Engineering. Her current research interest is in digital filters, multirate signal processing, and in communication applications of digital signal processing. She published more than 150 scientific papers and several book chapters all in the field of electrical engineering and digital signal processing. She is author of the book ‘Multirate Filtering for Digital Signal Processing: MATLAB Applications’. She is a senior member of IEEE and a member of The Academy of Engineering Sciences of Serbia. Miroslav D. Lutovac received the Dipl.-Eng., MSc and DSc degrees from the University of Belgrade in 1981, 1985 and 1991, respectively, all in Electrical Engineering. His research objectives are to automate the design and real-time implementation of analogue and digital signal processing systems, to develop the knowledge-based systems in the optimisation of various systems, and to transfer design tools and methodologies to industry. He is co-author of the monograph ‘Filter Design for Signal Processing Using MATLAB and Mathematica’ and the application package SchematicSolver. He is a senior member of IEEE and corresponding member of The Academy of Engineering Sciences of Serbia.