Calculation of all equivalent and canonic 2nd order digital filter structures

A method is presented to calculate all equivalent and canonic 2nd order digital filter structures. Equivalent means that all structures exhibit the same transfer function. Canonic stands for the minimum number of multipliers and delays. The investigation is confined to structures with four nodes and based on a matrix representation derived from flow-graph theory. Avoiding unrealizable delay free loops and disregarding structures which can only realize poles and zeros in restricted locations results in 3328 equivalent circuits with four nodes. Most of these circuits are new. A new circuit with low round-off noise and a dense pole grid is presented.