Pipelined CORDIC-based cascade orthogonal IIR digital filters

摘要

CORDIC-based cascade orthogonal infinite-impulse response (IIR) digital filters possess desirable properties for VLSI implementations such as local connection, regularity, absence of limit cycle and overflow oscillations, and good finite word-length behavior. However, the achievable sample rate of these filters is limited, since these structures cannot be pipelined at finer levels (such as bit or multi-bit level) due to the presence of feedback loops. In this paper, we present a novel approach to design pipelined CORDIC-based cascade orthogonal IIR digital filters using the transfer function approach. We first present a systematic way to synthesize cascade orthogonal IIR digital filters using scalar lossless inverse scattering theory, and realize the filter transfer function as a cascade inter-connection of orthogonal sections where each section implements one real zero or a pair of complex conjugate zeroes of the transfer function. In this way, the filter achieves low sensitivity over the entire filter spectrum. Novel pipelining techniques for both coarse-grain and fine-grain pipelining of these filters are then proposed. In coarse-grain pipelining, we present a novel method based on retiming and orthogonal matrix decomposition techniques which can increase the maximum filter sample rate to O(1) level which is independent of the filter order. In fine-grain pipelining, we present a novel method based on constraint filter design and polyphase decomposition techniques which could increase the maximum filter sample rate to any desired level. The proposed architecture for coarse-grain pipelining consists of only Givens rotations, and the one for fine-grain pipelining consists of only Givens rotations and a few additions. Both architectures can be realized using CORDIC arithmetic-based processors. Finally, finite word-length simulations are carried out to compare the performance of different topologies.