4D Bidirectional Lattice Digital Filters

A four-dimension (4D) bidirectional digital filter, having a minimum number of delay elements, is presented. This filter, besides having a minimum number of delay elements, also has an absolutely minimal state-space vector. Furthermore the transfer function, of the proposed 4D filter, is characterized by the all-pass property as in the well known classical one-dimension (1D) case. Four-dimension and two-dimension (2D) low-order examples are provided to show the features of the circuit and state-space realization structures.