A Bayesian Approach to the Restoration of Degraded Audio Signals

In this paper we derive the a posteriori probability for the location of bursts of noise additively superimposed on a Gaussian AR process. The theory is developed to give a sequentially based restoration algorithm suitable for real-time applications. The algorithm is particularly appropriate for digital audio restoration, where clicks and scratches may be modelled as additive bursts of noise. Experiments are carried out on both real audio data and synthetic AR processes and Significant improvements are demonstrated over existing restoration techniques. © 1995 IEEE

Dynamical symmetry of screened Coulomb potential and isotropic harmonic oscillator

It is shown that for the screened Coulomb potential and isotropic harmonic oscillator, there exists an infinite number of closed orbits for suitable angular momentum values. At the aphelion (perihelion) points of classical orbits, an extended Runge-Lenz vector for the screened Coulomb potential and an extended quadrupole tensor for the screened isotropic harmonic oscillator are still conserved. For the screened two-dimensional (2D) Coulomb potential and isotropic harmonic oscillator, the dynamical symmetries SO3 and SU(2) are still preserved at the aphelion (perihelion) points of classical orbits, respectively. For the screened 3D Coulomb potential, the dynamical symmetry SO4 is also preserved at the aphelion (perihelion) points of classical orbits. But for the screened 3D isotropic harmonic oscillator, the dynamical symmetry SU(2) is only preserved at the aphelion (perihelion) points of classical orbits in the eigencoordinate system. For the screened Coulomb potential and isotropic harmonic oscillator, only the energy (but not angular momentum) raising and lowering operators can be constructed from a factorization of the radial Schrodinger equation.

The vector fields admitting one-parameter spatial symmetry group and their reduction

For a n-dimensional vector fields preserving some n-form, the following conclusion is reached by the method of Lie group. That is, if it admits an one-parameter, n-form preserving symmetry group, a transformation independent of the vector field is constructed explicitly, which can reduce not only dimesion of the vector field by one, but also make the reduced vector field preserve the corresponding ( n - 1)-form. In partic ular, while n = 3, an important result can be directly got which is given by Me,ie and Wiggins in 1994.

Symmetry of chaotic attractors and kink-antikink structures in CMLs

In this paper the symmetries of coupled map lattices (CMLs) and their attractors are investigated by group and dynamical system theory, as well as numerical simulation, by means of which the kink-antikink patterns of CMLs in space-amplitude plots are discussed.