An algebra for signal processing
arXiv:1102.4205h-index: 5
Originality Synthesis-oriented
AI Analysis
This work provides a foundational framework for verifying signal processing algorithms, but remains theoretical and incremental.
The paper axiomatizes signal processing to enable exact computation and property verification, with Gaussian-based models allowing automated testing.
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.