Integration of a Generalized Ratio of Polynomials

This paper provides a closed-form solution to the indefinite integral of a ratio of generalized polynomials where the denominator polynomial is raised to the general order r∈Z+. Such an integral arises in physics and engineering, the solution of which allows for closed-form analysis.

Error Analysis of Neural Network with Multiply Neurons Using Rational Spline Weight Functions

In order to describe the generalization ability, this paper discusses the error analysis of neural network with multiply neurons using rational spline weight functions. We use the cubic numerator polynomial and linear denominator polynomial as the rational splines for weight functions. We derive the error formula for approximation, the results can be used to algorithms for training neural networks.

On Minimum Phase

We discuss the concept of `minimum phase' for scalar semi Hurwitz transfer functions. The latter are rational functions where the denominator polynomial has its roots in the closed left half complex plane. In the present note, minimum phase is defined in terms of the derivative of the argument function of the transfer function. The main tool to characterize minimum phase is the Hurwitz reflection. The factorization of a weakly stable transfer function into an all-pass and a minimum phase system leads to the result that any semi Hurwitz transfer function is minimum phase if, and only if, its numerator polynomial is semi Hurwitz. To characterize the zero dynamics, we use the Byrnes-Isidori form in the time domain and the internal loop form in the frequency domain. The uniqueness of both forms is shown. This is used to show in particular that asymptotic stable zero dynamics of a minimal realization of a transfer function yields minimum phase, but not vice versa.

VC++ and MATLAB-Based Interactive Filter Design

Filter designing is a work that most electronics engineers often do. In order to avoid editing cumbersome and duplicate MATLAB program every time when design a filter, now we design a filter designing software based on hybrid programming of VC++ and MATLAB. Users only need to enter the performance index; you can get to meet the requirements of the filter amplitude-frequency curve, phase-frequency curve, and the coefficients of the numerator and denominator polynomial of transfer function to achieve the filter design. Engine is implemented by VC++ and MATLAB mixed programming, making the interface friendly and program simple.

MIMO System Reduction Using Modified Pole Clustering and Genetic Algorithm

A new mixed method for reducing the order of the large-scale linear dynamic multi-input-multi-output (MIMO) systems has been presented. In this method, the common denominator polynomial of the reduced-order transfer function matrix is synthesized by using modified pole clustering while the coefficients of the numerator elements are computed by minimizing the integral square error between the time responses of the original and reduced system element using Genetic Algorithm. The modified pole clustering generates more dominant cluster centres than cluster centres obtained by pole clustering technique already available in literature. The proposed algorithm is computer-oriented and comparable in quality. This method guarantees stability of the reduced model if the original high-order system is stable. The algorithm of the proposed method is illustrated with the help of an example and the results are compared with the other well-known reduction techniques.

NEW Z-DOMAIN CONTINUED FRACTION EXPANSIONS BASED ON AN INFINITE NUMBER OF MIRROR-IMAGE AND ANTI-MIRROR-IMAGE POLYNOMIAL DECOMPOSITIONS

A magnitude response preserving modification of the denominator polynomial of a causal and stable digital transfer function leads to an infinite number of decompositions into a mirror-image polynomial (MIP) and an anti-mirror-image polynomial (AMIP). Properties and identifications of the MIP and AMIP are given. The identifications of Schussler and Davis, and the line spectral frequency formulation are special cases of the general MIP and AMIP decompositions introduced in this paper. Two types of Discrete Reactance Functions (DRF) are constructed. From these DRFs, five new continued fraction expansions (CFE) are developed, and some properties are obtained.

Mixed method of model reduction for uncertain systems

A mixed method for reducing a higher order uncertain system to a stable reduced order one is proposed. Interval arithmetic is used to construct a generalized Routh table for determining the denominator polynomial of the reduced system. The reduced numerator polynomial is obtained using factor division method and the steady state error is minimized using gain correction factor. The proposed method is illustrated using a numerical example.