Tarek I. Haweel

A new square wave transform based on the DCT

An efficient square wave transform (SWT) is presented. It is based on applying the signum function operator to the conventional discrete cosine transform (DCT) and is termed the signed DCT (SDCT). No order limits are imposed on the dimensions of the SDCT. Fast forward and backward transformation may be achieved. No multiplication operations or transcendental expressions are required. Analysis and simulations are introduced to show that the proposed SDCT maintains the good de-correlation and power compaction properties of the DCT. Simulation experiments are provided to justify the efficiency of the SDCT in signal processing applications such as system identification and image compression.

A simple variable step size LMS adaptive algorithm

A new LMS based variable step size adaptive algorithm is presented. The step size is incremented or decremented by a small positive value, whenever the instantaneous error is positive or negative, respectively. The algorithm is simple, robust and efficient. It is characterized by fast convergence and low steady state mean squared error. The performance of the algorithm is analysed for a stationary zero-mean white-Gaussian input. MC simulations are provided to demonstrate its improved performance over the conventional LMS (Proc. IEEE 1976; 64:1151–1162) and some other variable step size adaptive algorithms (IEEE Trans. Signal Process. 1992; 40:1633–1642; IEEE Trans. Signal Process. 1997; 45:631–639) within a range of statistical environments. For a non-stationary input, the proposed algorithm behaves similar to these algorithms. A modified version of the algorithm is presented to perform in the presence of abrupt changes. Copyright

A UNIVERSAL NEURAL NETWORK REPRESENTATION FOR HADRON–HADRON INTERACTIONS AT HIGH ENERGY

An efficient neural network (NN) has been designed to simulate the hadron–hadron interaction at high energy. Two cases have been considered simultaneously, the proton–proton (p–p) and the pion–proton (π-p) interactions. The neural network has been trained to produce the charged multiplicity distribution for both cases based on samples from the overlapping functions. The trained NN shows a good performance in matching the trained distributions. The NN is then used to predict the distributions that are not present in the training set and matched them effectively. The robustness of the designed NN in the presence of uncertainties, in the overlapping functions has been demonstrated.

Hadron–hadron interactions at high energy via Rademacher functions

Abstract Charged particles multiplicity distributions for hadron–hadron interactions at high energy have been studied. Two cases are considered: the proton–proton (p–p) and the pion–proton (π–p) interactions. The parton two-fireball model based on an impact parameter is adopted. The overlapping functions, known to be complicated and nonlinear, are approximated employing a series of Rademacher functions. The analysis has been facilitated, since Rademacher functions are linear, analytic and mathematically simple. The accuracy of the approximation is tunable through the order of the employed Rademacher functions. Theoretical expressions for inelastic cross-sections and the charged multiplicity distributions have been derived employing the proposed representation. Figures are provided to demonstrate good agreement between theoretical calculations and experimental data at different energies. Formulae for the change of some important parameters with the variation of high energy have been derived employing least square curve fitting techniques.

Adaptive least mean squares block Volterra filters

Adaptive filtering has found many applications in situations where the underlying signals are changing or unknown. While linear filters are simple from implementation and conceptual points of view, many signals are non-linear in nature. Non-linear filters based on truncated Volterra expansions can effectively model a large number of systems. Unfortunately, the resulting input auto-moment matrix is ill conditioned, which results in a slow convergence rate. This paper proposes a class of block adaptive Volterra filters in which the input sequences are Hadamard transformed to improve the condition number of the input auto-moment matrix and consequently improve the convergence rate. This is achieved by the decorrelation effect produced by the orthogonality of the transform. Since Hadamard transformation employs only ±1s, the additional required computational and implementation burdens are few. The effect of additive white Gaussian noise is introduced. Simulation experiments are given to illustrate the improved performance of the proposed method over the conventional Volterra LMS method. Copyright

Design of fixed point state space digital filters with low round-off noise

A simple method is described for the design of fixed-point recursive digital filters with low round-off noise. the method is based on reducing to zero as many as possible of the coefficients of the filter state matrices. an optimization procedure is used to get the optimum value of linear transformation that minimizes the total output round-off noise power. Compared with the existing approaches, this method is characterized by its computational simplicity, very low output round-off noise (if not the lowest possible) and low coefficient sensitivity. the structure of the proposed technique is modular, which makes it suitable for VLSI implementation. the technique is then employed to obtain a reduced-order low-round-off-noise filter with characteristics equivalent to some desired FIR specifications. Illustrative examples are given to verify these advantages.

Power series neural network solution for ordinary differential equations with initial conditions

Differential equations are very common in most academic fields. Modern digital control systems require fast on line and sometimes time varying solution schemes for differential equations. This paper presents new nonlinear adaptive numeric solutions for ordinary differential equations (ODE) with initial conditions. The main feature is to implement nonlinear polynomial expansions in a neural network-like adaptive framework. The transfer functions of the employed neural network follow a power series. The proposed technique does not use sigmoid or tanch non-linear transfer functions commonly adopted in conventional neural networks at the output. Instead, linear transfer functions are employed which leads to explicit power series formulae for the ODE solution. This allows extrapolation and interpolation which increase the dynamic numeric range for the solutions. The improved and accurate solutions for the proposed power series neural network (PSNN) are illustrated through simulated examples. It is shown that the performance of the proposed PSNN ODE solution outperforms existing conventional methods.

Adaptive power series solution for second order ordinary differential equations with initial conditions

Solution of differential equations is essential to analyze problems in many academic fields. Time varying solution schemes for differential equations are required in nonstationary environments. Numeric solutions are essential for nonlinear differential equations where explicit solutions do not exist, especially, for second and higher orders. This paper proposes efficient adaptive numeric solutions for second order ordinary differential equations (ODE) with initial conditions. The proposed technique implements neural networks with transfer functions that follow a power series. The proposed technique does not use sigmoid or tanch non-linear transfer functions commonly employed in conventional neural networks at the output. Instead, linear transfer functions are adopted which leads to explicit power series formulae for the ODE solution. This provides continuous solutions and enables interpolation and extrapolation. The efficient and accurate solutions provided by the proposed technique are illustrated through simulated examples. It is shown that the performance of the proposed technique outperforms existing conventional methods.

Adaptive multichannel LMS signal decoupling

Multichannel signal separation is a problem frequently encountered in many signal processing and communications applications. A simple and efficient sequential LMS adaptive multichannel signal decoupling algorithm is presented. It is based on minimizing the second commulant for the received mixed signals, although it can also be applied to minimize higher order commulants. The algorithm employs instantaneous signal cross products as estimates for the true cross-correlation based on ensemble averaging. No time averaging is required as in the case of most existing methods. The power of the decoupled output signals may be adjusted to the required levels. The proposed algorithm is fast, computationally efficient and suitable for real time applications. Analysis and simulations are provided to justify the efficiency of the proposed algorithm.

Adaptive harmonic estimation for power system protection

Many power system protection problems necessitate the measurement and track of the underlying current/voltage phasors. Adaptive LMS spectrum analyzers provide an ideal solution to such problems. This paper introduces a class of adaptive trigonometric spectrum analyzers. The underlying current/voltage is fed as a desired signal to an LMS adaptive algorithm. The reference input is a periodic regression derived from the basis set of the specified trigonometric discrete transform. The proposed algorithm is simple, computationally efficient, and exhibits a guaranteed stability and uniform convergence. A comparative study recommends the discrete Hartley transform. Simulations are provided to prove that the proposed spectrum analyzer is efficient in modeling faulty power system currents/voltages such as these arising from an over‐excitation of a power transformer.