avelet Transform has been successfully applied in different fields, ranging from pure mathematics to applied science. Numerous studies, carried out on Wavelet Transform, have proven its advantages in image processing and data compression and have made it a basic encoding technique in recent data compression standards. Pure software implementations of the Discrete Wavelet Transform, however, app...

Wavelet transform coding has been drawing much attention because of its ability to decompose images into a hierarchical structure that is suitable for adaptive processing in the transform domain. This paper presents an E$cient VLSI design of one-dimensional direct discrete wavelet transform processor. The proposed architecture computes three DWT stages and uses four parallel "lters. The archite...

In this paper, we introduce a novel algorithm to perform multi-scale Fourier transform analysis of piecewise stationary signals with application to automatic speech recognition. Such signals are composed of quasi-stationary segments of variable lengths. Therefore, in the proposed algorithm, signals are analyzed with multiple-sized windows. Resulting power spectra are then normalized such that t...

A new approach to derive transparent boundary conditions (TBCs) for wave, Schrödinger, heat and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physical reasonable and unreasonable solutions by the location of the singularities of the spatial Laplace transform of the exterior solution. To obtain a numerical algorithm, a Möbius transform is appli...

Omnidirectional cameras are versatile sensors that are able to provide a full 360-degree view of the environment. When combined with inertial sensing, omnidirectional vision offers a potentially robust navigation solution. However, to correctly fuse the data from an omnidirectional camera and an inertial measurement unit (IMU) into a single navigation frame, the 6-DOF transform between the sens...

A t ransform is introduced that maps cellular automata and discrete neural networks to dynamical systems on the unit interval. This transform is a topological conjugacy except at countably many points. In many cases, it gives rise to continuous full conjugates , in which case the transform preserves entropy. The transform also allows transfer of many dynamical properties of continuous systems t...

The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. The underlying motivation for performing this maneuver is as follows: the normalized power spectrum of the wave function is an excellent approximation (at small values of Planck’s constant—here a free parameter τ) to the density function of the distance transform gradients. Or...

In this paper we derive explicit inversion formulas for recovering scalar and vector fields supported on the unit disk from their 2D attenuated Radon transform in the framework of the fan-beam scanning geometry. The attenuation function is supposed to be known (from additional transmission measurements, for instance). It is known that in the vector case the kernel of the (unattenuated) Radon tr...

The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can satisfy numerically the energy and reconstruction theorems; however, transform pairs based on a variable window or nonuniform frequency sampling in general do no...

Let Hg and Dg be the Siegel upper half plane and the generalized unit disk of degree g respectively. Let C be the Euclidean space of all h× g complex matrices. We present a partial Cayley transform of the Siegel-Jacobi disk Dg × C (h,g) onto the Siegel-Jacobi space Hg × C (h,g) which gives a partial bounded realization of Hg × C (h,g) by Dg ×C . We prove that the natural actions of the Jacobi g...