4D Bidirectional Lattice Digital Filters

Abstract

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.