Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.

Adaptive windowed Fourier transform in 3-D shape measurement

Abstract: An adaptive windowed Fourier transform method in 3-D measurement based on a wavelet transform is proposed, in which, by applying a wavelet ridge, a series of scaling factors are calculated to determine the series of prime windows needed in the windowed Fourier transform method. Because the spectrum of each local fringe is simpler than that of the whole fringe, even though there is frequency aliasing as far as the whole fringe is concerned, the fundamental spectrum may separate into components in each local fringe. It is easy to filter out one of the fundamental frequency components from the local spectra. Adding these local fundamental components, the full fundamental component can be obtained correctly. The advantage of the method is that it not only eliminates the frequency aliasing, but also obtains the modulation distribution function to guide phase unwrapping.

An Explanation for the Logarithmic Connection between Linear and Morphological System Theory

Abstract: Dorst/van den Boomgaard and Maragos introduced the slope transform as the morphological equivalent of the Fourier transform. Generalising the conjugacy operation from convex analysis it formed the basis of a morphological system theory that bears an almost logarithmic relation to linear system theory; a connection that has not been fully understood so far. Our article provides an explanation by disclosing that morphology in essence is linear system theory in specific algebras. While linear system theory uses the standard plus-prod algebra, morphological system theory is based on the max-plus algebra and the min-plus algebra. We identify the nonlinear operations of erosion and dilation as linear convolutions in the latter algebras. The logarithmic Laplace transform makes a natural appearance as it corresponds to the conjugacy operation in the max-plus algebra. Its conjugate is given by the so-called Cramer transform. Originating from stochastics, the Cramer transform maps Gaussians to quadratic functions and relates standard convolution to erosion. This fundamental transform relies on the logarithm and constitutes the direct link between linear and morphological system theory. Many numerical examples are presented that illustrate the convexifying and smoothing properties of the Cramer transform.

An algebraic approach to symmetry detection

Abstract: We present an algorithm for detecting cyclic and dihedral symmetries of an object. Both symmetry types can be detected by the special patterns they generate in the object's Fourier transform. These patterns are effectively detected and analyzed using the "angular difference function" (ADF), which measures the difference in the angular content of images. The ADF is accurately computed by using the pseudo-polar Fourier transform, which rapidly computes the Fourier transform of an object on a near-polar grid. The algorithm detects all the axes of centered and non-centered symmetries. The proposed algorithm is algebraically accurate and uses no interpolations.

Accurate calculation of Fourier transform of two-center Slater orbital products†

Abstract: A method is presented which leads to accurate Fourier transform values of any 1s−1s Slater-type orbital overlap distribution. The numerical merits are discussed and illustrated by some examples.

Real Paley-Wiener theorems for the inverse Fourier transform on a Riemannian symmetric space

Abstract: We prove real Paley-Wiener theorems for the inverse Fourier transform on a semisimple Riemannian symmetric space G/K of the noncompact type. The functions on G/K whose Fourier transform has compact support are characterised by a L 2 growth condition. We also obtain real Paley-Wiener theorems for the inverse spherical transform.