Digital filter design by approximate time-domain modeling

Abstract

This thesis consists of two main parts. In the first part, two optimal Hankel methods: optimal Hankel without a D-term developed by Bettayed and optimal Hankel with a D-term developed by Glover, are applied to IIR (infinite impulse response) digital filter design and approximation. The results obtained from optimal Hankel methods are compared to the results obtained from other time-domain design methods: Least squares methods, CF method, balanced approximation methods, and suboptimal Hankel methods. Important conclusions are derived from this comparative study. Moreover, a slight modification is made to one of the optimal Hankel methods to improve its efficiency. The D-term which is neglected in this method is forced to be equal to the dc term of the impulse response. This improvement is shown by examples. In the second part, the two-sided approximation technique for IIR digital filter design is applied to the above methods. General formulae are derived so that any time-domain IIR digital filter design method could be applied using the two-sided approximation. It is shown through different examples that this technique gives a very efficient approximations to the desired magnitude response with low-order IIR digital filters compared to the one-sided approximation technique.