Propagation invariance is extended in the paraxial regime, leading to a generalized self-imaging effect. These wave fields are characterized by a finite number of transverse self-images that appear, in general, at different orientations and scales. They possess finite energy and thus can be accurately generated. Necessary and sufficient conditions are derived, and they are appropriately represe...

In this paper, we relate Poisson’s summation formula to Heisenberg’s uncertainty 1 principle. They both express Fourier dualities within the space of tempered distributions and 2 these dualities are furthermore the inverses of one another. While Poisson’s summation 3 formula expresses a duality between discretization and periodization, Heisenberg’s 4 uncertainty principle expresses a duality be...

Introduction Whereas ordinary functions on a locally compact group map the group elements into the complex numbers, a stochastic process can be understood as a mapping into a Hilbert space. The idea of a generalized function is to reduce the knowledge about the function to that of certain averages. It leads to the concept of generalized functions as continuous linear functionals on spaces of te...

An analytical solution to the transient heat conduction for a two dimensional cylindrical fin with general boundary conditions is obtained by the principle of superposition and separation variables. In the analysis, homogeneous material properties and thickness, the convective heat transfer coefficient, the ambient temperature and the fin properties are assume to be constant. The closed form tr...

This study of occupation time densities for continuous-time Markov processes was inspired by the work of E.Nir et al (see [13]) in the field of Single Molecule FRET spectroscopy. There, a single molecule fluctuates between two or more states, and the experimental observable depends on the state’s occupation time distribution. To mathematically describe the observable there was a need to calcula...

We present a novel local-based face verification system whose components are analogous to those of biological systems. In the proposed system, after global registration and normalization, three eye regions are converted from the spatial to polar frequency domain by a Fourier-Bessel Transform. The resulting representations are embedded in a dissimilarity space, where each image is represented by...

A new LFM-signal detector formulated by the integration of the 4th-power modulus of the fractional Fourier transform is proposed. It has similar performance to the modulus square detector of Radon-ambiguity transform because of the equivalence relationship between them. But the new detector has much lower computational complexity in the case that the number of the searching angles is far less t...

A hybrid modeling framework for scattering from general 3D elastic targets in a stratified ocean waveguide is presented, incorporating multiple scattering between the target and the stratification, and allowing for targets to be completely or partially buried in a stratified seabed. The approach uses a generalized wavefield superposition, or virtual source approach, together with a Fourier-Bess...

One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric structure of the underlying graph data domain. In this paper, we generalize one of the most important signal processing tools windowed Fourier analysis to the...