This paper presents a fast “two-dimensional Fourier continuation” (2D-FC) method for construction of biperiodic extensions smooth nonperiodic functions defined over general two-dimensional domains. The approach, which runs at cost (\mathcalO(N?og N)\) operations an $N$-point discretization grid, can be directly generalized to domains any given dimensionality, but such generalizations are not co...

Glossary WT1D The one-dimensional Wavelet Transform as defined in [1]. See also [2] in this volume. WT2D The two-dimensional Wavelet Transform. Discrete Ridgelet Trasnform (DRT) The discrete implementation of the continuous Ridgelet transform. Fast Slant Stack (FSS) An algebraically exact Radon transform of data on a Cartesian grid. First Generation Discrete Curvelet Transform (DCTG1) The discr...

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...

Abstract In this paper, we introduce the two-sided fractional quaternion Fourier transform (FrQFT) and give some properties of it. The main results paper are divided into three parts. Firstly a definition FrQFT. Secondly based on QFT, study relationship between QFT FrQFT, differential FrQFT Parseval identity. Finally, an example to illustrate application its inverse in solving partial equations.

An overview is given to a new approach for obtaining generalized Fourier transforms in the context of hypercomplex analysis (or Clifford analysis). These transforms are applicable to higher-dimensional signals with several components and are different from the classical Fourier transform in that they mix the components of the signal. Subsequently, attention is focused on the special case of the...

Utilizing the asymptotic method of stationary phase, I derive expressions for the Fourier transform of a two-dimensional fringe pattern. The method assumes that both the amplitude and the phase of the fringe pattern are well-behaved differentiable functions. Applying the limits in two distinct ways, I show, first, that the spiral phase (or vortex) transform approaches the ideal quadrature trans...

Although the spectrum of radially periodic images is often expressed in terms of finite or infinite series of Bessel functions, such expressions do not clearly reveal the exact impulsive structure of the spectrum. An alternative Fourier decomposition of radially periodic images, in terms of circular cosine functions, is presented, and its significant advantages are shown. It is shown that the F...