Most of the computer codes for the recent simulation studies of geodynamo are based on a spectral transform method in which variables are expanded in spherical harmonics. This method, however, is not suitable for high-resolution simulations because of a large amount of computation for spectral transform with respect to Legendre functions. In this study, we developed a modified code based on the...

Let Fq be the finite field with q elements and let ! be a primitive n-th root of unity in an extension eld Fqd of Fq. Given a polynomial P 2 Fq[x] of degree less than n, we will show that its discrete Fourier transform (P (1); P (!); :::; P (!n¡1)) 2Fqd n can be computed essentially d times faster than the discrete Fourier transform of a polynomial Q 2 Fqd[x] of degree less than n, in many case...

Abstract. In this paper we study the behaviour at infinity of the Fourier transform of Radon measures supported by the images of fractal sets under an algorithmically random Brownian motion. We show that, under some computability conditions on these sets, the Fourier transform of the associated measures have, relative to the Hausdorff dimensions of these sets, optimal asymptotic decay at infini...

It is well-known that an image can be reconstructed from an infinite set of moments. Many works have focused on the reconstruction aspects of orthogonal moments, and have shown that the image can be reconstructed easily from a finite set of orthogonal moments. However, reconstruction ability of geometric moments is not yet proved. In this paper, the inverse problem of geometric moments is addre...

Under certain conditions on an integrable function P having a real-valued Fourier transform P̂ and such that P(0)=0, we obtain an estimate which describes the oscillation of P̂ in [−C‖P ′‖∞/‖P ‖∞, C‖P ′‖∞/‖P ‖∞], whereC is an absolute constant, independent of P. Given > 0 and an integrable function with a non-negative Fourier transform, this estimate allows us to construct a finite linear combina...

Stationary Fourier transform spectrometry is an interesting concept for building reliable field or embedded spectroradiometers, especially for the mid- and far- IR. Here, a very compact configuration of a cryogenic stationary Fourier transform IR (FTIR) spectrometer is investigated, where the interferometer is directly integrated in the focal plane array (FPA). We present a theoretical analysis...

We define a Fourier transform S for the quantum double D(G) of a finite group G. Acting on characters of D(G), S and the central ribbon element of D(G) generate a unitary matrix representation of the group SL(2, Z). The characters form a ring over the integers under both the algebra multiplication and its dual, with the latter encoding the fusion rules of D(G). The Fourier transform relates the...

The time-to-frequency-domain conversion is often required in many applications of the finite-difference time-domain (FDTD) method. This paper presents a new FDTD time-to-frequencydomain conversion algorithm based on the optimization of nonuniform fast Fourier transform (NUFFT) with several redundancy-reduction techniques. The proposed algorithm can perform the FDTD conversion at multiple desire...

(3) v = fdju + vc for the decomposition into discrete (ƒ dju as above) and continuous vc parts. Let F = û = J2k' + J'e' dvc{y) be the Fourier transform of the measure v. Then Wiener's theorem says (2) continues to hold. This means that the Fourier transform vc of the continuous portion of the measure does not contribute to the Bohr mean of |F|. We will interpret Wiener's theorem to mean that ev...

Abstract. We consider Linsker’s neural network model, in particular, development of oriented receptive fields of cells on layer G, and investigate which features in this model are crucial for the development. We assume that the correlation function is a Mexican-hat shape function while we introduce the arbor function explicitly and discuss its role in the development. We compute the Fourier tra...