Applying the Z-transform for the static analysis of floating-point numerical filters

2007/06/02 by David Monniaux, Monniaux, David
Computer Science · Physics and Astronomy · #Digital Filter Design and Implementation #FOS: Computer and information sciences #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Programming Languages (cs.PL)

paper · pdf · doi:10.48550/arxiv.0706.0252

openalex publication_date 2007/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Verification of Magnitude and Phase Responses in Fixed-Point Digital Filters
• Verifying Fixed-Point Digital Filters using SMT-Based Bounded Model Checking
• Sliding Z Transform: Applications to convolutive blind source separation
• Recursive Filters as Linear Time-Invariant Systems
• Advancements in Signal Processing and Control Systems Using Z and L-Transforms