Orthogonal chirp division multiplexing for coherent optical fiber communications

In this paper, we propose an orthogonal chirp division multiplexing (OCDM) technique for coherent optical communication. OCDM is the principle of orthogonally multiplexing a group of linear chirped waveforms for high-speed data communication, achieving the maximum spectral efficiency (SE) for chirp spread spectrum, in a similar way as the orthogonal frequency division multiplexing (OFDM) does for frequency division multiplexing. In the coherent optical (CO)-OCDM, Fresnel transform formulates the synthesis of the orthogonal chirps; discrete Fresnel transform (DFnT) realizes the CO-OCDM in the digital domain. As both the Fresnel and Fourier transforms are trigonometric transforms, the CO-OCDM can be easily integrated into the existing CO-OFDM systems. Analyses and numerical results are provided to investigate the transmission of CO-OCDM signals over optical fibers. Moreover, experiments of 36-Gbit/s CO-OCDM signal are carried out to validate the feasibility and confirm the analyses. It is shown that the CO-OCDM can effectively compensate the dispersion and is more resilient to fading and noise impairment than OFDM.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Power system parameters forecasting using Hilbert-Huang transform and machine learning

A novel hybrid data-driven approach is developed for forecasting power system parameters with the goal of increasing the efficiency of short-term forecasting studies for non-stationary time-series. The proposed approach is based on mode decomposition and a feature analysis of initial retrospective data using the Hilbert-Huang transform and machine learning algorithms. The random forests and gradient boosting trees learning techniques were examined. The decision tree techniques were used to rank the importance of variables employed in the forecasting models. The Mean Decrease Gini index is employed as an impurity function. The resulting hybrid forecasting models employ the radial basis function neural network and support vector regression. A part from introduction and references the paper is organized as follows. The second section presents the background and the review of several approaches for short-term forecasting of power system parameters. In the third section a hybrid machine learningbased algorithm using Hilbert-Huang transform is developed for short-term forecasting of power system parameters. Fourth section describes the decision tree learning algorithms used for the issue of variables importance. Finally in section six the experimental results in the following electric power problems are presented: active power flow forecasting, electricity price forecasting and for the wind speed and direction forecasting.