Systolic pipeline architectures for symmetric convolutions

Symmetries in the coefficients of common types of finite-impulse response (FIR) digital filters can be utilized to enable systolic pipeline realizations with considerable reduction in the number of multiplier stages. To obtain a concise description of the interconnections of these pipeline structures, a recursive state variable representation is presently developed. The representation is then utilized to examine the effects of symmetry on pipeline structures for discrete convolutions in one and two dimensions. For common types of one-dimensional filters, such as bandpass, phase-shift (Hilbert transform), and edge detector (differentiator) types, the number of multipliers may be approximately halved using odd/even symmetry. For common types of two-dimensional filters, such as bandpass, rho filters (tomographics), and edge detector (Laplacian) types, the number of multipliers can be reduced by approximately a factor of eight