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

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.