Title :
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
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;
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
DOI :
10.1109/TFSA.1998.721388
