Analogue filter group delay optimization using a stochastic approach

An analogue filter group delay response is optimized using art all-pass network connected in the cascade of the filter. This contribution introduces an original method of all-pass network correction designing of using a random-based approach. The main objective of the method is the calculation of an optimal all-pass network order and optimal coefficients of its transfer function. To realize this objective it is necessary to find minima of so-called optimization spaces. The spaces definition provides an important generalization of the optimization task. The original stochastic approach is used to find the mentioned minima of the spaces. The minima can be detected using several probability densities. The method combines advantages of a numerical approach with rigorous analytical pre-processing. Compared to current optimization methods, the described approach provides very good convergence, velocity and especially independence from the initial estimation of the all-pass network transfer function coefficients. The original objective function ensures absolutely stable convergence in the multidimensional optimization spaces. This objective function was developed with regard to properties of the analogue filters. The designed method is illustrated by a few practical optimizations. A well-known circuit simulator, Micro-Cap, is used as a comparative system because of its relatively good optimization algorithm. All the presented original algorithms and functions are debugged in the MATLAB environment. Copyright (C) 2009 John Wiley & Sons, Ltd.