Digital Filters and Signal Processing
Digital Filters and Signal Processing
Linear analysis and optimization of stream programs
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
Ten methods to bound multiple roots of polynomials
Journal of Computational and Applied Mathematics
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
Modeling, optimization and computation for software verification
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Automatic modular abstractions for linear constraints
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Interval slopes as a numerical abstract domain for floating-point variables
SAS'10 Proceedings of the 17th international conference on Static analysis
Modular abstractions of reactive nodes using disjunctive invariants
APLAS'11 Proceedings of the 9th Asian conference on Programming Languages and Systems
A generic ellipsoid abstract domain for linear time invariant systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
A bit too precise? bounded verification of quantized digital filters
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Acceleration of the abstract fixpoint computation in numerical program analysis
Journal of Symbolic Computation
Abstract acceleration of general linear loops
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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Digital linear filters are used in a variety of applications (sound treatment, control/command, etc.), implemented in software, in hardware, or a combination thereof. For safety-critical applications, it is necessary to bound all variables and outputs of all filters. We give a compositional, effective abstraction for digital linear filters expressed as block diagrams, yielding sound, precise bounds for fixed-point or floating-point implementations of the filters.