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Sensitivity-Based Pole and Input-Output Errors of Linear Filters as Indicators of the Implementation Deterioration in Fixed-Point Context

Abstract

Input-output or poles sensitivity is widely used to evaluate the resilience of a filter realization to coefficients quantization in an FWL implementation process. However, these measures do not exactly consider the various implementation schemes and are not accurate in general case. This paper generalizes the classical transfer function sensitivity and pole sensitivity measure, by taking into consideration the exact fixed-point representation of the coefficients. Working in the general framework of the specialized implicit descriptor representation, it shows how a statistical quantization error model may be used in order to define stochastic sensitivity measures that are definitely pertinent and normalized. The general framework of MIMO filters and controllers is considered. All the results are illustrated through an example.

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Correspondence to Thibault Hilaire.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Hilaire, T., Chevrel, P. Sensitivity-Based Pole and Input-Output Errors of Linear Filters as Indicators of the Implementation Deterioration in Fixed-Point Context. EURASIP J. Adv. Signal Process. 2011, 893760 (2011). https://doi.org/10.1155/2011/893760

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Keywords

  • Error Model
  • General Framework
  • Implementation Scheme
  • Sensitivity Measure
  • Implementation Process