On higher order approximations for hermite-gaussian functions and discrete fractional Fourier transforms


Candan C.

IEEE SIGNAL PROCESSING LETTERS, vol.14, no.10, pp.699-702, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 10
  • Publication Date: 2007
  • Doi Number: 10.1109/lsp.2007.898354
  • Title of Journal : IEEE SIGNAL PROCESSING LETTERS
  • Page Numbers: pp.699-702

Abstract

Discrete equivalents of Hermite-Gaussian functions play a critical role in the definition of a discrete fractional Fourier transform. The discrete equivalents are typically calculated through the eigendecomposition of a commutator matrix. In this letter, we first characterize the space of DFT-commuting matrices and then construct matrices approximating the Hermite-Gaussian generating differential equation and use the matrices to accurately generate the discrete equivalents of Hermite-Gaussians.