Minimax design of recursive digital filters

The application of two new algorithms for minimax optimization due to Charalambous and Bandler is investigated. The application is to the problem of finding the coefficients of a recursive digital filter to meet arbitrary specifications of the magnitude or the group delay characteristics. Unlike the original minimax algorithm due to Bandler and Charalambous in which a sequence of least $\text{p}\text{th}$ optimizations as $\text{p}$ tends to infinity is taken, the two new algorithms do not require the value of $\text{p}$ to do this. Instead, a sequence of least $\text{p}\text{th}$ optimization problems is constructed with finite values of $\text{p}$ in the range $\text{1 < p < ∞}$. A criterion is given under which the order of the filter can be increased by growing filter sections. A general computer program has been developed, based on the ideas presented.