ANALYSIS OF LIMIT CYCLES BY MEANS OF AFFINE ARITHMETIC COMPUTER-AIDED TESTS (WedPmPO1)

Author(s) : Juan Antonio López (Dep. Ingeniería Electrónica, Univ. Politécnica de Madrid, Spain) Gabriel Caffarena (Dep. Ingeniería Electrónica, Univ. Politécnica de Madrid, Spain) Carlos Carreras (Dep. Ingeniería Electrónica, Univ. Politécnica de Madrid, Spain) Octavio Nieto-Taladriz (Dep. Ingeniería Electrónica, Univ. Politécnica de Madrid, Spain)

Abstract : 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.

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