Design of fast 3-D frequency planar and frequency beam recursive digital filters

Abstract

By exploring parallelism, new three-dimensional discrete recursive filter structures are proposed, developed, and investigated for implementing a class of 3-D Frequency Planar and 3-D Frequency Beam recursive filters. It is shown that these new structures are suitable for high-speed, real-time applications. Three-dimensional discrete ladder form structures using discrete differentiators, based on 1-D ladder signal flow graph simulation, are proposed. Elemental pre-distortion and signal flow graph manipulation techniques are presented to eliminate the delay-free loops in the discrete signal flow graph topology without altering the transfer function, leading to very simple 3-D discrete filter structures. Three-dimensional discrete direct-differentiator form structures are proposed and developed by means of a novel frequency transformation. These 3-D recursive filter structures directly realize the filter transfer functions and offer a high operating speed. The effect of the 3-D bilinear frequency warping on the class of 3-D Frequency Planar and Frequency Beam recursive filters is investigated and a 3-D pre-warping design technique is proposed. It is shown that characteristics of the 3-D bilinear frequency warping are very different from those found in the 1-D and 2-D cases. Examples of simulations are given in both 3-D spatial-temporal-domain and 3-D frequency-domain to verify that the proposed 3-D recursive filter structures have he required characteristics.