Realization of 4D lattice-ladder digital filters

A circuit realization is presented for four-dimensional (4D) lattice-ladder 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. An educational conjointment of 4D lattice filters with lower dimension filters (2D, 1D), is imparted.