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Niveau: Supérieur, Doctorat, Bac+8

Static Analysis of Digital Filters 1 Jerome Feret Departement d'Informatique de l'Ecole Normale Superieure, 75230 PARIS Cedex 5, FRANCE Abstract We present an Abstract Interpretation-based framework for automatically analyz- ing programs containing digital filters. Digital filtering consists in implementing numerical recursions: the value of a variable S (the output) is computed from a fixed finite number of the last consecutive values of the variable S and from a fixed finite number of the last consecutive values of another variable E (the input). Our framework allows us to refine existing analyses so that they can handle given classes of digital filters. We only have to design a class of symbolic properties that describe the invariants throughout filter iterations and to describe how these properties are transformed by filter iterations. Then, the analysis allows both inference and proofs of the properties about the program variables that are tied to any such filter. In case of linear filters, we propose a systematic method for designing the abstract domain by using interval and elliptic constraints. Key words: Abstract Interpretation, symbolic domains, numerical domains, digital filtering, synchronous systems, critical systems, embedded systems. 1 Introduction Digital filters are widely used in real-time embedded systems (as found in au- tomotive, aeronautic, and aerospace applications) since they allow modeling behaviors previously ensured by analogical filters into software .

Static Analysis of Digital Filters 1 Jerome Feret Departement d'Informatique de l'Ecole Normale Superieure, 75230 PARIS Cedex 5, FRANCE Abstract We present an Abstract Interpretation-based framework for automatically analyz- ing programs containing digital filters. Digital filtering consists in implementing numerical recursions: the value of a variable S (the output) is computed from a fixed finite number of the last consecutive values of the variable S and from a fixed finite number of the last consecutive values of another variable E (the input). Our framework allows us to refine existing analyses so that they can handle given classes of digital filters. We only have to design a class of symbolic properties that describe the invariants throughout filter iterations and to describe how these properties are transformed by filter iterations. Then, the analysis allows both inference and proofs of the properties about the program variables that are tied to any such filter. In case of linear filters, we propose a systematic method for designing the abstract domain by using interval and elliptic constraints. Key words: Abstract Interpretation, symbolic domains, numerical domains, digital filtering, synchronous systems, critical systems, embedded systems. 1 Introduction Digital filters are widely used in real-time embedded systems (as found in au- tomotive, aeronautic, and aerospace applications) since they allow modeling behaviors previously ensured by analogical filters into software .

- abstract domains
- variable sn
- real numbers
- digital filtering
- refining interval
- using elliptic
- filter
- constraints

Sujets

Informations

Publié par | profil-zyak-2012 |

Nombre de lectures | 13 |

Langue | English |

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