In the paper, an analysis of the state-of-the-art of active elements for analog signal processing is presented which support - in contrast to the conventional operational amplifiers - not only the voltage-mode but also the current- and mixed-mode operations. Several problems are addressed which are associated with the utilization of these elements in linear applications, particularly in frequency filters. A methodology is proposed which generates a number of fundamentally new active elements with their potential utilization in various areas of signal processing.