From the rectangular to the quincunx Gabor lattice via fractional Fourier transformation

Transformations of Gabor lattices have been associated with operations on the window functions that arise in Gabor theory. In particular, it has been shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function, which plays an important role as a window function in Gabor theory, is an eigenfunction of fractional Fourier transformation, this transformation has a clear advantage over other operations that are used to transform a rectangular lattice into a quincunx lattice.