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A new analytical expression for the optical transfer function of multiple-scattering media such as clouds, mists, and dust aerosols is given in terms of their microphysical characteristics. The geometrical optics approximation is used to find local optical parameters of a scattering medium, including the simple approximation of the phase function, which is the key to the solution of the problem considered here. The optical transfer function is taken within a small-angle approximation of the radiative transfer theory. A comparison with Monte Carlo data shows a fairly satisfactory accuracy of our analytic formulas. Key words: Radiative transfer theory, small-angle approximation optical transfer function, geometrical optics.

Control of the welding process is a very important step in welding automation. Since the welding process is complex and highly nonlinear, it is very difficult to accurately model the process for real-time control. In this research, a discrete-time transfer function matrix model for gas metal arc welding process is proposed. This empirical model takes the common dynamics for each output and inherent process and measurement delays into account. Although this linearized model is valid only around the operating point of interest, the adaptation mechanism employed in the control system render this model useful over a wide operating range. Since welding is inherently a nonlinear and multi-input, multi-output process, a multivariable adaptive control system is used for high performance. The process outputs considered are weld bead width and depth, and the process inputs are chosen as the travel speed of the torch and the heat input. A one-step-ahead (or deadbeat) adaptive control algorithm combined with a recursive least-squares methods for on-line parameter estimation is implemented in order to achieve the desired weld bead geometries. Control weighting factors are used to maintain the stability and reduce excessive control effort. Some guidelines for the control design are also suggested. Command following and disturbance rejection properties of the adaptive control system for both SISO and MIMO cases are investigated by simulation and experiment. Although a truly independent control of the outputs is difficult to implement because of a strong output coupling inherent in the process, a control system for simultaneous control of bead width and depth was successfully implemented.

A new technique for pilot estimations of both high- and low-altitude processes on a flight simulator, in the presence of atmospheric turbulence, provides marked elevation of the simulator's motion response to disturbances. An ordinary second-order transfer function simulation of the aircraft is adequate in the motion elevation pathway. This technique enhances disturbance-induced simulator motion and increases heave specific force levels without over-stepping the travel constraints of the motion system in the presence of a pilot in the loop.

Delayed block transfer function incorporated in the frequency domain helps identify signal components in the input window and estimate transfer functions. The transfer functions are used to derive the properties of a complete transfer system. Theoretical expressions representing bias errors in the functions are derived.

A novel Josephson Inductive Kinetic Amplifier (IKA), which is more sensitive than the traditional dc superconducting quantum interference device, is developed to determine weak dc magnetic fields with low noise. IKA operation involves parametric amplifications subsequent to frequency shifting of dc input to a high frequency range. The IKA transfer function is derived from an analytical theory used to obtain the stability, frequency response and optical parameters of the system.

An algorithmic framework which decoupled the nonlinear criterion was proposed to optimally recognize rational transfer function parameters from the input-output data of discrete-time linear systems. The nonlinear criterion was decoupled into a linear and nonlinear problem for evaluating the optimal numerator and optimal denominator, respectively. This algorithm's framework, which has a decoupled approach, decreased the system's computational requirements.

The stability of the algorithm is influenced by errors in the estimation of the cancellation path transfer function for active noise and vibration control systems implementing the filtered-x LMS algorithm. Errors change the maximum stable value of convergence coefficient through an inverse proportional relationship. The algorithm is stable if the error does not exceed plus or minus 90 degrees.

A novel method that included an operator transformation was proposed to solve problems related to transfer function approximation of a continuous-time dynamic system in the presence of colored noise. The method facilitated interpretation of transfer function results and yielded estimates for continuous-time transfer function coefficient values.

Knowledge of system eigensolutions is not essential for novel numerical and analytical modeling and synthesis of complex distributed parameter systems. The approach is applicable to non-self-adjoint systems with homogeneous boundary conditions. It can be used to predict system eigensolutions.

In this paper, we present a modified method for generating multiparameter root loci of both continuous and discrete time systems. A more practical computational method for plotting the robust root locus is developed. The graph of the locations of the poles of the transfer function of the closed-loop system corresponding to each gain can be plotted readily and accurately with this method. The sensitivity of poles to the coefficients of the characteristic polynomial can thus be examined, and the appropriate tuning gain selected to achieve a better robustness. Also, a stricter bound of the zeros of the characteristic polynomial is given to further reduce the complexity of the computation of the robust root locus. The technique is applied to the design of robotic manipulators. Simulations of controller design for the PUMA 762 robot disk grinding process are included.

We derived the transfer function for a white-light interferometric sensor based on highly birefringent (HB) fiber, assuming that both sensing and receiving interferometers are dispersive. This transfer function indicates that different responses to changes in the measurand may be observed depending on whether displacement of the contrast function or the interference fringes is detected. In the first case the sensitivity of the sensor is determined by the influence of the measurand on modal polarization dispersion while in the second case it depends on the influence of the measurand on modal birefringence of the HB fiber. This sensitivity difference limits the operation range of recently proposed zero-order fringe- tracking methods within which the unambiguous measurement is possible. The dispersion effects for a white-light interferometric strain sensor composed of York HB or Andrew E-type fiber as a sensing element and a quartz Wollaston prism as a receiving interferometer were studied experimentally. Sensitivities of modal polarization dispersion, modal birefringence, and chromatic dispersion of modal birefringence to the strain were determined for both types of sensing fiber. For these specific combinations of sensing/receiving interferometers we also determined the unambiguous measurement range for zero-order fringe-tracking techniques.

An M-channel pseudo-quadrative mirror filter (QMF) design scheme limits the initial QMF as a linear-phase spectral factor of a filter, resulting in delayof system transfer function. The scheme yields pseudo-QMF bank designs with aminus 100 decibel stopband attenuation. The scheme derives an aliasingcancellation limit that cancels out all dominant aliasing errors.

This paper presents an introduction to concepts and applications of transfer function identification in power systems. The paper begins with a brief introduction to transfer function identification methods using least-squares approaches and then discusses applications which include SVC's, model validation applications, and software validation. A comparison is also made between eigenvalues obtained from transfer function identification and small signal analysis. Methods for testing the validity of identified transfer functions are also discussed.

This note analyzes the sensitivity of transfer functions w.r.t. finite wordlength effect errors in the implementation of the coefficients of both shift operator and delta operator parameterizations. The relationships between optimal realization sets in shift and delta operator are established. It is shown that the optimal realizations in delta operator have better performance than those in shift operator when the poles of the systems are clustered around Zeta = +1. A numerical example is given.

Thetraditional transfer function approach is compared to a recursive estimation procedure that allows the model to change over time in order to pinpoint and estimate transfer functions models relating leading indicators to the Swedish index of industrial production. Results of the comparison show that the recursive method is useful. It was also found that estimates of the model parameters indeed change over time.

We describe the use of Hubble Space Telescope Fine Guidance Sensor transfer scans to characterize telescope alignment. To accomplish this we developed a software system to extract the aberration content from the observed transfer scans. The transfer scans show large aberration levels that do not originate in the telescope. The appearance of significant coma in the transfer scans has been identified as resulting from the shearing of spherical aberration caused by a beam misalignment within the Fine Guidance Sensors themselves.

A least squares approach for automatic transfer function synthesis in the frequency domain is introduced. An alternative to existing techniques for system identification, it facilitates easier learning for controls students. It works by maintaining a minimum value for the error between the inverse transfer function and the inverse of the frequency response measurements. It includes a weighting scheme that enables an improved low-frequency fit.

There is an increasing need in physiology to estimate nonparametric linear transfer functions from data originating from biological systems which are invariably nonlinear. For pseudorandom (PRN) input stimuli, we derive general expressions for the apparent transfer (Z) and coherence (gamma squared) functions of nonlinear systems that can be represented by a Volterra series. It is shown that in the case of PRN signals in which the frequency components are integer multiples of other components the estimates of Z are seriously biased due to harmonic distortion and crosstalk among frequency components of the input. When the PRN signal includes components that are not integer multiples of other components harmonic distortion is avoided, but not necessarily cross talk. Here the estimates of Z remain poor without a noticeable influence on gamma squared. To avoid the problems associated with harmonic distortions and minimize the influence of crosstalk, a family of pseudorandom signals is proposed which are especially suited for the estimation of Z and gamma squared in mechanical measurements of physiological systems at low frequencies. The components in the signals cannot be reproduced as linear combinations of two or more frequency components of the input. In a second-order system, this completely eliminates the bias, while in higher-order, but not strongly nonlinear systems, the interactions among the components are reduced to a level that the response can be considered as if it was measured with independent sine waves of an equivalent amplitude. It is also shown that the values of gamma squared are not appropriate to assess linearity of the system. The theory is supported by simulation results and experimental examples brought from the field of respiratory mechanics by comparing the input impedance of the respiratory system of a dog measured with various PRN signals.

This note presents a simplified approach to Bode's theorem for both continuous-time and discrete-time systems, along with some generalization. For continuous-time systems, the constraints of open-loop stability and roll-off at s = infinity are removed. A counter example shows that, when the excess poles / zeros vanishes, the Bode integral drops from infinite to finite value when the open-loop gain crosses a critical value. A revised result is also developed in this note. The salient feature of this approach is that at no stage do we invoke either Cauchy's theorem or the Poisson integral; the simplified proof relies only on elementary analysis. This approach carries over to the discrete-time case in a straightforward manner.

For strongly stabilizable systems for which a strongly stabilizing controller is known approximately, we consider system identification in the graph, gap, and chordal metrics using robust H(sub infinity) identification of the closed-loop transfer function in the framework proposed by Helmicki, Jacobson, and Nett. Error bounds are derived showing that robust convergence is guaranteed and that the identification can be satisfactorily combined with a model reduction step. Two notions of robust identification of stable systems are compared, and an alternative robust identification technique based on smoothing, which can be used to yield polynomial models directly, is developed.

This note has derived a criterion for no unstable discrete zeros in terms of coefficients of a continuous-time transfer function and of a sampling period when a continuous-time, stable, and strictly proper plant is sampled. It is also shown that the shortest sampling period ensuring minimum-phase behavior can be calculated from a simple equation.

A new algorithm to compute the coprime matrix fraction description from a given transfer function matrix W(s) is presented in this note. The algorithm is based on Householder transformations to compute the minimal realization of W(s) and on the orthogonal version of Wolovich-Falb's structure theorem to determine the coprime form. The proposed method is numerically less expensive than a like algorithm available in the literature, which has used singular value decomposition.

We discuss the realization of highly efficient fan-out elements. Laser-beam writing lithography is available now for fabricating smooth surface relief microstructures. We develop several methods for optimizing microstructure profiles. Only a small number of parameters in the object plane are necessary for determining the kinoform. This simplifies the calculation of M x N arrays also for large M and N. Experimental results for a 9-beam fan-out element are presented.

This paper is probably the first to describe algorithms suited to the efficient calculation of both proper and non-proper transfer function zeros of linearized dynamic models for large interconnected power systems. The paper also describes an improvement to the well known AESOPS algorithm, formulating it as an exact transfer function zero finding problem which is efficiently solved by a Newton-Raphson iterative scheme. Large power system results are presented in the paper.

The intensities and resolutions at the diffraction focus of optical systems with rotationally symmetric minimum-variance aberration functions as well as functions with slight variations from this shape and a prescribed fixed maximum deviation value at the edge of the exit pupil are calculated for circular and annular exit pupils. The results for the intensity at the diffraction focus obtained either by numerical integration of the diffraction integral or by using the Marechal formula show that the maxima of these intensities are achieved for optical systems with wave aberration functions of minimum variance, thus verifying the Marechal criterion. The resolutions first zeros of the intensities in the radial direction) at this diffraction focus are also presented. Key words: Optical design, aberration.

Diffractive lenses differ from conventional optical elements in that they can produce more than one image because of the presence of more than one diffraction order. These spurious, defocused images serve to lower the contrast of the desired image. We show that a quantity that we define as the integrated efficiency serves as a useful figure of merit to describe diffractive lenses. The integrated efficiency is shown to be the limiting value for the optical transfer function; in most cases it serves as an overall scale factor for the transfer function. We discuss both monochromatic and polychromatic applications of the integrated efficiency and provide examples to demonstrate its utility.

The important transfer functions are derived for a constant-frequency current-programmed switching dc-to-dc converter with an input filter. From these transfer functions, design criteria are developed to ensure stability and prevent converter performance degradation.

Previous results on estimating errors or error bounds on identified transfer functions have relied upon prior assumptions about the noise and the unmodeled dynamics. This prior information took the form of parameterized bounding functions or parameterized probability density functions, in the time or frequency domain with known parameters. Here we show that the parameters that quantify this prior information can themselves be estimated from the data using a maximum likelihood technique. This significantly reduces the prior information required to estimate transfer function error bounds. We illustrate the usefulness of the method with a number of simulation examples. The paper concludes by showing how the obtained error bounds can be used for intelligent model order selection that takes into account both measurement noise and under-modeling. Another simulation study compares our method to Akaike's well-known FPE and AIC criteria.

A new approach for implementation of full-wave precision rectifiers in CMOS technology is presented. The most distinguishing feature of this approach is that the rectification is performed in current domain while both input and output signals are voltages. The rectifier has a very simple structure and both noninverting and inverting circuits can be realized with one op-amp, two current mirrors, and six MOS transistors. The performances of the proposed rectifiers are analyzed and discussed. Extensive computer simulation and experimental results obtained with this and other types of precision rectifiers, which demonstrate many advantages of the proposed techniques over others, are presented.

The theorem on minimal factorization of rational matrix functions without a pole or zero at infinity is extended to arbitrary rational matrix functions. To obtain this generalization, the concept of a centered realization for possibly nonproper rational matrix function is developed. A centered realization involves a single state-space operator and has most properties of a usual state-space realization.

In this note it is shown that the Hilbert-Schmidt-Hankel norm (HSH-norm) of a transfer function of a stable system is equal, up to a constant factor, to the square root of the area enclosed by the oriented Nyquist diagram of the transfer function (multiplicities included). A generalization is presented for the case of systems which have no poles on the stability boundary, but otherwise have no restrictions on the pole locations.

We describe a model-based method for estimating the spatial frequency response of a digital-imaging system (e.g., a CCD camera) that is modeled as a linear, shift-invariant image acquisition subsystem that is cascaded with a linear, shift-variant sampling subsystem. The method characterizes the two-dimensional frequency response of the image acquisition subsystem to beyond the Nyquist frequency by accounting explicitly for insufficient sampling and the sample - scene phase. Results for simulated systems and a real CCD-based epifluorescence microscopy system are presented to demonstrate the accuracy of the method., A proposed method for estimating the spatial frequency response of a digital-imaging system such as a charge-coupled device camera is designed as a linear, shift-invariant image acquisition subsystem cascaded with a sampling subsystem with the same features. The method is two-dimensional and estimates the image acquisition subsystem's response beyond the Nyquist frequency by recording multiple images of the object. Simulations show that the method can produce accurate descriptions of frequency characteristics of high-performance epifluorescence microscopy imaging systems.

A study was made to assess the effects of high-temperature gradients on sound transmission in an acoustic probe tube. The tube has its probe sensing end located in the hot environment and the transducer located at the cool end. The results show that a theoretically derived transfer-function can be used to correct acoustic data measured by a high-temperature probe tube. Moreover, the transfer-function model must have visco-thermal effects in the probe tube in order to be accurate. Agreement between the computed and measured attenuation is good over the frequency range from 0.4 to 6 kilohertz, with some discrepancies occurring at attenuation minima.

Theorem 3.3 of the above paper contains some errors, which are discussed in this note. Consequently the necessary corrections are presented. Index Terms--Algebraic Riccati equation, [H.sub.[infinity]] norm, internal stabilization, positive semidefinite matrix, transfer function matrix.

The consequence of the coupling of a charged particle with a polarization field is the formation of a quasi-particle called the 'polaron'. The degree of 'localization' of such charge depends on the nature of this coupling. In this way, trapping at an atomic scale is described as resulting from the evolution of a coupling involving successively: the electronic polarization field, the infrared polarization field, and the quasi-static ionic polarization field. The internal energy stored in the surrounding medium polarized by the charge is high because the charge is so well localized. The maximum of this energy is obtained for the quasi-static polarization field; its magnitude is of the order of 5 to 10 eV per trapped charge. This work addresses the physics of aging and of the breakdown process on the basis of an unsustainable increase in local internal energy within the material, due to charge trapping - the polarization around a trapped charge increases the local energy; the relaxation of the material lattice then follows a rapid detrapping of charges from their sites, releasing the local excess site region energy into the material. Such a release executes transient virtual work on the material, producing macroscopic dielectric damage, and when critical, unstable conditions are achieved in the time domain, this is followed by electrical breakdown. This interpretation of electrical material breakdown is related to bulk breakdown as observed in thin film laminate structures (~ [[micro]meter]) and surface flashover as seen in large structures (~ mm to cm).

This paper presents two new transfer matrices for an inverse potential problem using boundary element methods. The condition numbers of the new transfer matrices are compared with that of the conventional transfer matrix through numerical examples. It is shown that the condition number of the new transfer matrices may be several orders of magnitude smaller than that of the conventional one. The regularized solutions achieved by using the new transfer matrices are also shown to be better than the usual one.

It is known that useful two-dimensional (2-D) and three-dimensional (3-D) discrete-domain recursive transfer functions may be designed by applying the MD bilinear transformation to the continuous-domain transfer functions of prototype MD inductance-resistance networks. Closed-form expressions are derived for the impulse responses of these 2- and 3-D discrete-domain filters.

This note deals with the problem of extrema which may occur in the step-response of a linear system with stable real zeros and poles. We give a simple sufficient condition to avoid extrema using the pole-zero configuration of the corresponding transfer-function.

Structural damage method uses active member transfer function information, in coordination with artificial neural network, to detect damages in various structures. The neural network training uses the pole/zero transfer function data to specify damage measurements and predict the level of damage in the structure. The efficacy and validity of the method are demonstrated in a 10-bar truss structure.

The transfer function of a separable-in-denominator 2-D digital filter is not necessarily valid for a filter with complex poles in both the z1 and z2 independent variables. Modified equations and relevant results on quantization error evaluations are presented. These quantization errors are due to quantization at the filter input.

Using a communication channel model, we prove the known theorem that the Jones matrix of a system for backward propagation is the transpose of that for forward propagation. This result, together with the transformation of a coordinate system for opposite propagation directions, is shown to be useful for analyzing the round-trip wave propagation in nonreciprocal media.

Phase-inhomogeneous optical crystals, slightly rough surfaces, and turbulence in a liquid are studied by measuring the transverse-coherence function. A new polarization interferometer for measuring the coherence function is suggested that ensures high accuracy of the measurement.

The objective of this work is to bring to control literature the strengthened and symmetric version of the classical Rouche's form. This symmetric form has been discovered by Glicksberg [1], [2] and was first employed in [3] to determine a robust dead time for closed-loop stability. In this note we motivate the need for Rouche's forms as a tool for the analysis of linear time-invariant control systems. A robustness criterion is given and its corresponding geometrical interpretation is obtained. A simplified implementation of the symmetric form is obtained and its relation to passivity is highlighted. Finally, an application to time delay systems is given.

Byline: Mathew Hu, Jiju Antony Transfer functions, one of the core components in Design for Six Sigma (DFSS) which provide the needed relationships between design, process and materials parameters, and the Critical-to-Quality (CtQ characteristics) in the product and process development cycle. Transfer function provides a direct method for understanding and representing an overall product and process function. Transfer function also provides a strategy for customer voice cascade, function decomposition, physical modelling, and concept generation. The concept of transfer function is not new. However, the development of transfer function is not trivial and is a creative and challenging task. Developing a proper transfer function in DFSS framework will facilitate earlier decision-making and enhance the 'designing it right the first time'.