Design for optimum classical filters

Filter optimisation is the improvement of one or more characteristics of a filter. Such improvement is beneficial to the design in some sense. The work request focuses on the magnitude response of classical filters that are polynomial approximations to the ideal ´brick-wall´ filter. Given a set of passband and stopband frequency requirements, optimisation then becomes the achievement of any combination of the following criteria while maintaining filter order fixed: maximisation of the band-edge selectivity; minimisation of the passband ripple; maximisation of the stopband attenuation. Such optimisation results in new pole/zero locations that implement the above features without increasing filter complexity. A graphical technique for specifying optimum filters in the above sense is presented exploiting the special capability of filter nomographs. Tradeoffs in the criteria above are related to critical pole-pair Q and filter delay responses. A design example is presented to illustrate the power and ease of designing classical filters with optimum magnitude responses.