130,345 research outputs found
Formalization of Transform Methods using HOL Light
Transform methods, like Laplace and Fourier, are frequently used for
analyzing the dynamical behaviour of engineering and physical systems, based on
their transfer function, and frequency response or the solutions of their
corresponding differential equations. In this paper, we present an ongoing
project, which focuses on the higher-order logic formalization of transform
methods using HOL Light theorem prover. In particular, we present the
motivation of the formalization, which is followed by the related work. Next,
we present the task completed so far while highlighting some of the challenges
faced during the formalization. Finally, we present a roadmap to achieve our
objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201
Towards the Formalization of Fractional Calculus in Higher-Order Logic
Fractional calculus is a generalization of classical theories of integration
and differentiation to arbitrary order (i.e., real or complex numbers). In the
last two decades, this new mathematical modeling approach has been widely used
to analyze a wide class of physical systems in various fields of science and
engineering. In this paper, we describe an ongoing project which aims at
formalizing the basic theories of fractional calculus in the HOL Light theorem
prover. Mainly, we present the motivation and application of such formalization
efforts, a roadmap to achieve our goals, current status of the project and
future milestones.Comment: 9 page
Some fundamental properties on the sampling free nabla Laplace transform
Discrete fractional order systems have attracted more and more attention in
recent years. Nabla Laplace transform is an important tool to deal with the
problem of nabla discrete fractional order systems, but there is still much
room for its development. In this paper, 14 lemmas are listed to conclude the
existing properties and 14 theorems are developed to describe the innovative
features. On one hand, these properties make the N-transform more effective and
efficient. On the other hand, they enrich the discrete fractional order system
theor
Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)
Oxford, UK, 26 August 200
The near shift-invariance of the dual-tree complex wavelet transform revisited
The dual-tree complex wavelet transform (DTCWT) is an enhancement of the
conventional discrete wavelet transform (DWT) due to a higher degree of
shift-invariance and a greater directional selectivity, finding its
applications in signal and image processing. This paper presents a quantitative
proof of the superiority of the DTCWT over the DWT in case of modulated
wavelets.Comment: 15 page
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