Design of first-order differentiator utilising FIR and IIR sub-filters

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.