A Geometric Approach to Group Delay Network Synthesis
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All-pass networks with prescribed group delay are used for analog 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-of-the-art methods in comparison examples.
KeywordsAll-pass circuits, approximation problem, analog signal processing, delay ripple equalisation, group delay engineering, linear phase filters
Document typePeer reviewed
Document versionFinal PDF
SourceRadioengineering. 2016 vol. 25, č. 2, s. 351-364. ISSN 1210-2512
- 2016/2