Osuch, Piotr JanStander, Tinus2016-08-052016-08-052016-06Osuch, PJ & Stander, T 2016, 'A geometric approach to group delay network synthesis', Radioengineering, vol. 25, no. 2, pp. 351-3641210-2512 (print)1805-9600 (online10.13164/re.2016.0351http://hdl.handle.net/2263/56217All-pass networks with prescribed group delay are used for analogue signal processing and equalisation of transmission channels. The state-of-the-art methods for synthesising quasi-arbitrary group delay functions using all-pass elements lack a theoretical synthesis procedure that guarantees minimum-order networks. We present an analytically-based solution to this problem that produces an all-pass network with a response approximating the required group delay to within an arbitrary minimax error. For the first time, this method is shown to work for any physical realisation of second-order all-pass elements, is guaranteed to converge to a global optimum solution without any choice of seed values as an input, and allows synthesis of pre-defined networks described both analytically and numerically. The proposed method is also demonstrated by reducing the delay variation of a practical system by any desired amount, and compared to state-ofthe- art methods in comparison examples.enThe Radioengineering Journal is an open access journal. This work is licensed under a Creative Commons Attribution 3.0 Unported License.All-pass circuitsApproximation problemAnalogue signal processingDelay ripple equalisationGroup deley engineeringLinear phase filtersArticle