Multidimensional wave field signal theory: Mathematical foundationsNatalie Baddour
- AIP Advances, January 2011, American Institute of Physics
- DOI: 10.1063/1.3596359
Are you using Fourier or Hankel transforms with the wave equation? This article can help.
What is it about?
This article gives six kick-ass results for integrals needed for inverse Fourier or Hankel transforming expressions when using the wave equation in 1, 2 or 3 dimensions.
Why is it important?
Single or multidimensional Fourier/Hankel transforms applied to the wave equation make manipulations easy. The hard part is inverse transforming back out of the Fourier/Hankel domain. This paper provides some integral results that help with this inverse transformation for a large class of problems. 1D, 2D polar and 3D spherical polar coordinates in particular are considered.