Unified Architectures for Parallel Cyclic Convolution and Reduced Complexity Parallel FIR Filtering

Novel recursive formulations of Block Pseudocirculant Matrices, which are reordered using stride permutations, lead to fully structured higher order Block Pseudocirculants, termed Super Block Pseudocirculant Matrices. These matrices provide a unified framework to develop highly modular parallel cyclic convolution architectures as well as to develop reduced complexity parallel FIR filtering constructs. These architectures can be considered duals of each other in the cyclic and linear (FIR) convolution contexts respectively. The proposed approach is easily scalable, highly modular, and unifies both architectures through a matrix-based universal technique that provides further theoretical understanding and gives additional flexibility to the designer.