The Euler transformation is a linear sequence transformation to accelerate the convergence of an alternating series. The sequence of weights of the transformation is extended to a continuous weight function which can accelerate Fourier type integrals including Hankel transforms with a slowly convergent integrand. We show that the continuous weight function can also be used to compute the Fourie...

To date, a number of numerical methods, including the popular Finite-Difference Time Domain (FDTD) technique, have been proposed to simulate Ground-Penetrating Radar (GPR) responses. Despite having a number of advantages, the finite-difference method also has pitfalls such as being very time consuming in simulating the most common case of media with high dielectric permittivity, causing the for...

PURPOSE Analytical phantoms have closed form Fourier transform expressions and are used to simulate MRI acquisitions. Existing three-dimensional (3D) analytical phantoms are unable to accurately model shapes of biomedical interest. The goal of this study was to demonstrate that polyhedral analytical phantoms have closed form Fourier transform expressions and can accurately represent 3D biomedic...

In our last work, we formulate a Fourier transformation on the infinitedimensional space of functionals. Here we first calculate the Fourier transformation of infinite-dimensional Gaussian distribution exp ( −πξ ∞ −∞ α 2(t)dt ) for ξ ∈ C with Re(ξ) > 0, α ∈ L2(R), using our formulated Feynman path integral. Secondly we develop the Poisson summation formula for the space of functionals, and defi...

In this work, the method of Fourier descriptors has been extended to produce a set of normalized coefficients which are invariant under any affine transformation (translation, rotation, scaling, and shearing). The method is based on a parameterized boundary description which is transformed to the Fourier domain and normalized there to eliminate dependencies on the affine transformation and on t...