Realization of 4D lattice structured digital filters

This paper presents a circuit realization for four-dimensional (4D) lattice discrete filters. The proposed 4D circuit realization requires, for its implementation, a minimum number of delay elements. Further, the dimension of the state-vector, of the derived 4D state space model, is minimal and its 4D transfer function is characterized by the all-pass property. A step-by-step low-order example is provided to demonstrate the proposed minimality of both, circuit, and state space realizations.