Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Revisiting the 1D and 2D Laplace Transforms

Version 1 : Received: 11 July 2020 / Approved: 12 July 2020 / Online: 12 July 2020 (15:46:45 CEST)

How to cite: Ortigueira, M.D.; Machado, J.T. Revisiting the 1D and 2D Laplace Transforms. Preprints 2020, 2020070266 (doi: 10.20944/preprints202007.0266.v1). Ortigueira, M.D.; Machado, J.T. Revisiting the 1D and 2D Laplace Transforms. Preprints 2020, 2020070266 (doi: 10.20944/preprints202007.0266.v1).

Abstract

This paper reviews the unilateral and bilateral, one- and two-dimensional Laplace transforms. The unilateral and bilateral Laplace transforms are compared in the one-dimensional case, leading to the formulation of the initial-condition theorem. This problem is solved with all generality in the one- and two-dimensional cases with the bilateral Laplace transform. General two-dimensional linear systems are introduced and the corresponding transfer function defined.

Subject Areas

Laplace transform; Two-dimensional Laplace transform; Initial-conditions; Two-dimensional linear systems

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