Modulated Oscillations in Three Dimensions

The analysis of the fully three-dimensional and time-varying polarization characteristics of a modulated trivariate, or three-component, oscillation is addressed. The use of the analytic operator enables the instantaneous three-dimensional polarization state of any square-integrable trivariate signal to be uniquely defined. Straightforward expressions are given which permit the ellipse parameters to be recovered from data. The notions of instantaneous frequency and instantaneous bandwidth, generalized to the trivariate case, are related to variations in the ellipse properties. Rates of change of the ellipse parameters are found to be intimately linked to the first few moments of the signal's spectrum, averaged over the three signal components. In particular, the trivariate instantaneous bandwidth---a measure of the instantaneous departure of the signal from a single pure sinusoidal oscillation---is found to contain five contributions: three essentially two-dimensional effects due to the motion of the ellipse within a fixed plane, and two effects due to the motion of the plane containing the ellipse. The resulting analysis method is an informative means of describing nonstationary trivariate signals, as is illustrated with an application to a seismic record.Comment: IEEE Transactions on Signal Processing, 201

Estimation de la fréquence instantanée des signaux FM par opérateur d'énergie Psi_B

Psi_B energy operator is an extension of the cross Teager-Kaiser energy operator which is an non-linear energy tracking operator to deal with complex signals and its usefulness for non-stationary signals analysis has been demonstrated. In this letter two new properties of Psi_B are established. The first property is the link between Psi_B and the dynamic signal which is a generalization of the Instantaneous Frequency (IF). The second property obtained for frequency modulated signals is a simple way to estimate the IF. These properties confirm the interest of Psi_B operator to track the non-stationary of a signal. Results of IF estimation in noisy environment of a non-linear FM signal are presented and comparison to Wigner-Ville distribution and Hilbert transform-based method is provided

Modelling of Path Arrival Rate for In-Room Radio Channels with Directive Antennas

We analyze the path arrival rate for an inroom radio channel with directive antennas. The impulse response of this channel exhibits a transition from early separate components followed by a diffuse reverberation tail. Under the assumption that the transmitter's (or receiver's) position and orientation are picked uniformly at random we derive an exact expression of the mean arrival rate for a rectangular room predicted by the mirror source theory. The rate is quadratic in delay, inversely proportional to the room volume, and proportional to the product of beam coverage fractions of the transmitter and receiver antennas. Making use of the exact formula, we characterize the onset of the diffuse tail by defining a "mixing time" as the point in time where the arrival rate exceeds one component per transmit pulse duration. We also give an approximation for the power-delay spectrum. It turns out that the power-delay spectrum is unaffected by the antenna directivity. However, Monte Carlo simulations show that antenna directivity does indeed play an important role for the distribution of instantaneous mean delay and rms delay spreadComment: Submitted to IEEE Trans. Antennas and Propagatio

Large eddy simulations and direct numerical simulations of high speed turbulent reacting flows

The primary objective of this research is to extend current capabilities of Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS) for the computational analyses of high speed reacting flows. Our efforts in the first two years of this research have been concentrated on a priori investigations of single-point Probability Density Function (PDF) methods for providing subgrid closures in reacting turbulent flows. In the efforts initiated in the third year, our primary focus has been on performing actual LES by means of PDF methods. The approach is based on assumed PDF methods and we have performed extensive analysis of turbulent reacting flows by means of LES. This includes simulations of both three-dimensional (3D) isotropic compressible flows and two-dimensional reacting planar mixing layers. In addition to these LES analyses, some work is in progress to assess the extent of validity of our assumed PDF methods. This assessment is done by making detailed companions with recent laboratory data in predicting the rate of reactant conversion in parallel reacting shear flows. This report provides a summary of our achievements for the first six months of the third year of this program

Geometric Quantum Computation

We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. Thus quantum geometrical phases can form the basis of any quantum computation. Moreover, as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the potential of a naturally fault-tolerant way of performing quantum computation.Comment: 15 pages, LaTeX, uses cite, eepic, epsfig, graphicx and amsfonts. Accepted by J. Mod. Op