Rectangular-to-quincunx Gabor lattice conversion via fractional Fourier transformation

Author

Bastiaans, Martin J. ; Van Leest, Arno J.

Author_Institution

Fac. Elektrotech., Eindhoven Univ. of Technol., Netherlands

fYear

1998

Firstpage

169

Lastpage

172

Abstract

The fractional Fourier transformation is used to transform the rectangular Gabor lattice into a quincunx lattice. By using the isometric property of the unitary fractional Fourier transformation, the biorthogonality relation for the rectangular lattice is transformed into a relation which holds for the quincunx lattice. Since a Gaussian function, which plays an important role as a window function in Gabor theory, is an eigenfunction of the fractional Fourier transformation, this transformation has a clear advantage over other operations that are used to transform a rectangular lattice into a quincunx lattice

Keywords

Fourier transforms; Gaussian processes; eigenvalues and eigenfunctions; signal sampling; Gabor´s signal expansion; Gaussian function; biorthogonality relation; eigenfunction; fractional Fourier transformation; isometric property; quincunx lattice; rectangular lattice; rectangular-to-quincunx Gabor lattice conversion; sampling lattice; Chirp; Eigenvalues and eigenfunctions; Fourier transforms; Geometry; Kernel; Lattices; Sampling methods; Signal synthesis; Time frequency analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Time-Frequency and Time-Scale Analysis, 1998. Proceedings of the IEEE-SP International Symposium on

Conference_Location

Pittsburgh, PA

Print_ISBN

0-7803-5073-1

Type

conf

DOI

10.1109/TFSA.1998.721388

Filename

721388