Int. J. Metrol. Qual. Eng.
Volume 12, 2021
|Number of page(s)||12|
|Published online||18 March 2021|
Convolution and deconvolution: two mathematical tools to help performing tests in research and industry
Electricity & Magnetism, LNE, Paris, France
2 ECAM-EPMI, Cergy-Pontoise, France
* Corresponding author: firstname.lastname@example.org
Accepted: 10 February 2021
The concepts of convolution and deconvolution are well known in the field of physical measurement. In particular, they are of interest in the field of metrology, since they can positively influence the performance of the measurement. Numerous mathematical models and computer developments dedicated to convolution and deconvolution have emerged, enabling a more efficient use of experimental data; this in sectors as different as biology, astronomy, manufacturing and energy industries. The subject finds today a new topicality because it has been made accessible to a large public for applications such as processing photographic images. The purpose of this paper is to take into account some recent evolutions such as the introduction of convolution methods in international test standards. Thus, its first part delivers a few reminders of some associated definitions. They concern linear systems properties, and integral transforms. If convolution, in most cases, does not create major calculation problems, deconvolution on the contrary is an inverse problem, and as such needs more attention. The principles of some of the methods available today are exposed. In the third part, illustrations are given on recent examples of applications, belonging to the domain of electrical energy networks and photographic enhancement.
Key words: convolution / deconvolution / metrology / electrical networks
© J.-P. Fanton, published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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