Periodic Look Ahead Filter Design for Pipelining 2-D IIR Digital Filters

Pipelining is a means of obtaining fast sampling and processing speed in hardware implementation of digital systems. A look ahead scheme is required for the pipelined system. Although methods and algorithms for pipelining one-dimensional (1-D) IIR (infinite impulse response) filter have been developed in the past twenty years, there has been few results on pipelining two-dimensional (2-D) IIR filters. In this paper, we construct a general look ahead scheme for 2-D IIR filters. While analyzing the difficulty in the design of stable LTI (linear time-invariant) 2-D look ahead filters, we develop a periodic stabilization method such that stable pipelined 2-D IIR filters can be obtained analytically. Based on this periodic stabilization method, a numerical algorithm can be proposed to design a stable periodic pipelined filters with possible minimum computation complexity. All the results developed in this paper can be applied to the pipelining of all kinds of 2-D IIR digital operators, for example 2-D digital controllers.