The fractional Fourier transformation is used to transform the rectangular Gabor lattice into a quin-cunx lattice. By using the isometric property of the unitary fractional Fourier transformation, the biorthog-onality 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 func...

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processin...

In this paper, we examine the accuracy of several calculation methods for iron loss of rotating machines using the finite element method. Two calculation methods are compared with the measurements. One is based on the Fourier transformation of the flux density waveforms at each finite element. The other is the direct calculation from the waveforms without Fourier transformation. It is clarified...

Computation of integrals of strongly oscillating functions is one of the more important problems of numerical analysis, because such integrals are encountered in applications in many branches of mathematics as well as in other science such as quantum physics, flow mechanics and electromagnetism. Main examples of strongly oscillating integrands are encountered in different transformation, for ex...