TL;DR
This paper proposes an algebraic framework for signal processing aiming to formalize algorithms in an idealized setting and translate them effectively to real-world applications.
Contribution
It introduces axioms and models based on Gaussian functions for exact computation and automated property testing in signal processing.
Findings
Models enable exact computation of signal algorithms.
Framework supports automated testing of algorithm properties.
Axiomatization bridges ideal and real-world signal processing.
Abstract
Our paper presents an attempt to axiomatise signal processing. Our long-term goal is to formulate signal processing algorithms for an ideal world of exact computation and prove properties about them, then interpret these ideal formulations and apply them without change to real world discrete data. We give models of the axioms that are based on Gaussian functions, that allow for exact computations and automated tests of signal algorithm properties.
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Taxonomy
TopicsImage and Signal Denoising Methods · Mathematical Analysis and Transform Methods · Digital Filter Design and Implementation