ANALYSIS OF LIMIT CYCLES BY MEANS OF AFFINE ARITHMETIC COMPUTER-AIDED TESTS

摘要

Modern analysis of the finite word-length properties of DSP algorithms is typically carried out using CAD tools. The objectives of this paper are threefold: (ⅰ) to show that affine arithmetic is specially well-suited for quantization analysis of digital filters; (ⅱ) to present a new tool based on multiple-precision affine arithmetic elements that allows fast characterization of the signal ranges in linear systems; and (ⅲ) to develop an exhaustive-search algorithm that detects limit cycles and requires less computation time than existing approaches. Final comparative results confirm the validity of the limit cycles detection algorithm on second-order shift and delta-operator realizations.