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Complex phase, asymptotic parameter and integrals
  • Nicolas Vacca,
  • Pierre Argoul
Nicolas Vacca

Corresponding Author:[email protected]

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Pierre Argoul
Laboratoire Ville Mobilité Transport, Université Gustave Eiffel


Asymptotic signals have been introduced to approximate integrals with the stationary phase approximation. However, the deviation between integrals and their approximations is not bounded without further constraints. We propose an alternative with the introduction of a parameter defined in the complex phase representation. The magnitude of this new parameter controls the local harmonicity of the signal. It therefore controls the deviation between integrals and their approximations, which do not rely on the stationary phase principle. Approximations of Fourier transforms illustrate the results. The parameter is also involved in additional properties of diverse nature.
30 May 2024Submitted to TechRxiv
07 Jun 2024Published in TechRxiv