A two-stage angle-rotation architecture and its error analysis for efficient digital mixer implementation

Abstract

An efficient angle-rotation architecture, suitable for use in a digital mixer, is presented. The architecture employs a decomposition of the high-precision rotation-angle into a coarse angle and a fine angle, and employs two processing stages, coarse and fine. Only the coarse stage employs a ROM, and that ROM is extremely small. Small multipliers are shown to suffice while providing full accuracy at the system output. A systematic development of the architecture and its supporting theory and assumptions is given, along with the rationale for determining its structure. A rigorous analysis of its error sources is presented, as well as the computation of bounds for the various errors they induce at the system output. This error analysis is shown to lead to a straightforward means of designing an efficient two-stage angle-rotation unit for a digital mixer, given input/output bitwidths and performance specifications.