4D FIR digital filter realizations

This paper proposes generalized circuit and state space realizations for four-dimensional (4D) Finite Impulse Response (FIR) filters. Specifically, lattice and direct-form filter structures are considered. The 4D circuit realizations utilize, for their implementation, a minimum number of delay elements. Further, the dimensions of the state-space vector, of the formulated 4D state space models, are minimal. Examples are given to demonstrate the minimality of their circuit and state-space realizations.