Novel 2-D cascade ladder-lattice structure recursive digital filters

Abstract

We present in this paper a novel cascade ladder-lattice structure of two-dimensional (2-D) recursive digital filters; this cascade based on two delay units M and N and a basic lattice section. Our new realization has a minimal number of basic lattice sections. Using a transfer function representation; the matrix representations for the basic lattice sections are proposed and used to derive the transfer functions of the realized 2-D digital lattice filters. The theory and transfer functions of the realized 2-D lattice Digital filter are derived. We use the 2-D Givone–Roesser’s state space model to verify the minimal realization of the proposed 2-D recursive digital filte; this later gives matrix-vectors A, b, c and a scalar d which are derived. As result, the dimension of the 2-D generalized state space model is minimal. Finally, several design examples are provided for conducting illustration.