Concept Of Transfer Function Research Articles

Invariant representations of discrete-time periodic systems

In this paper we overview, compare and elaborate on the invariant representations of periodic systems. Precisely, with reference to discrete-time systems, we first introduce the concept of periodic transfer function from which a notion of generalized frequency response can be worked out. Then we discuss the following four reformulations: (i) time lifted, (ii) cyclic, (iii) frequency lifted and (iv) Fourier. A number of interesting links will be established, and many theoretical aspects somewhat overlooked in the existing literature will be clarified. All reformulations are first worked out from the input–output description and then elaborated in a state-space formalism.

Associated H∞-Problem For Sampled-Data Systems

On basis of the parametric transfer function concept an useful expression of the ℋ∞-norin for rather general sampled-data systems is derived. The present paper shows how this norm can be used to formulate the associated ℋ∞-problem for digital controllers at continuous-time plants. The chosen cost functional covers continuous-time system behaviour. The solution is given on basis of the Laplace transformation in continuous time and the theory of polynomial equations. The presented approach allows to handle the problem directly in the frequency domain with the possibility of a numerical solution.

Wavelength-dependent measurement and evaluation of surface topographies: application of a new concept of window roughness and surface transfer function

The technological performance of surfaces in fields such as tribology, biocompatibility and optics is often highly dependent on surface topography and roughness. The common practice of applying `integral' roughness parameters, however, is often an incomplete and unsatisfactory way to describing surface topographies. Wavelength-dependent roughness evaluation is shown to be a successful method for the description of surface topographies in various characteristic roughness ranges, as well as being a useful indicator of the effect of surface treatment processes. This study examined the effects of common cut-off (COF) (high- and low-frequency) and average filtering (AFT) as well as fast Fourier transformation (FFT) techniques, as applied to synthetic and experimental profiles. Furthermore, the relationship between the roughness value R q and the amplitudes C n of the FFT power spectrum is demonstrated. To characterise a particular surface treatment process consisting of several consecutive processes, a surface treatment transfer function is defined using individual FFT coefficients C n x for each surface treatment step. To illustrate the application for industrial surfaces, two-dimensional (2-D) profiles on a micromachined steel surface (calibration sample) as well as on lacquered car body sheet and titanium implant surfaces were measured with a non-contact laser profilometer (LPM) and evaluated. FFT is shown to be a powerful method for the calculation of the wavelength-dependent roughness, as well as for the back-transformation of partial data sets into profiles in predefined wavelength ranges (“window roughness”). The more conventional filter methods give similar results, but some information are lost due to the fact that they do not correspond to a set of orthonormal functions. The concept of wavelength-dependent (“window”) roughness parameters is demonstrated to be a concept that allows for a much more detailed description of surface topographical properties with two main merits: (a) it allows macroscopic physico-technological properties to be correlated with roughness contributions in selected wavelength ranges; (b) the overall effect of consecutive surface treatment processes can be separated into wavelength-dependent contributions from each treatment step. The concept is demonstrated for consecutive surface treatment processes in the pretreatment and lacquering of aluminium car body sheet and for blasting and etching processes in the case of titanium medical implants.

Roles of propagating and evanescent waves in solid immersion lens systems

The electromagnetic field incident on the thin-film layers in a solid immersion lens (SIL) system is decomposed into contributions from homogeneous and inhomogeneous waves, which are commonly referred to as propagating and evanescent waves, respectively. The homogeneous and the inhomogeneous parts have different properties with respect to the field distribution in the gap and inside the recording layers. The homogeneous part is shown to diffract like a focused wave with a numerical aperture of 1, and the inhomogeneous part decays exponentially away from the bottom of the SIL. Two examples are discussed in detail, and the concept of a vector illumination system transfer function, which includes effects of the recording layers, is introduced.

Relativistic calculations of intensity distributions in elemental maps using contrast transfer functions.

The interpretation of highly resolved elemental maps is not straightforward: one has to consider the quantum mechanical nature of the scattering process as well as the influence of the microscope. Existing calculations of the contrast in elemental maps are based on a non-relativistic approach, while in most of the currently installed electron microscopes, the electrons penetrate the specimen with relativistic energies >/= 200 keV. Therefore, we have recalculated the intensity distribution in elemental maps based on a fully relativistic theory. Using the concept of contrast transfer functions, the simulations account for lens aberrations as well as the defocus. Surprisingly, the results exhibit considerable deviations between the relativistic and non-relativistic calculations even in the region of low acceleration voltages such as 100 kV. These differences increase with increasing acceleration voltage and are strongly dependent on aperture and energy loss. Quantitative simulations and evaluations of highly resolved elemental maps should therefore make use of a fully relativistic theory.

Monitoring of power transformers using the transfer function method

Summary form only given as follows. The transfer function concept is well known as an additional method of evaluating the impulse test of power transformers in the test laboratory. Another application for this method is monitoring of power transformers in service. According to the method of how to measure transient signals for the calculation of transfer functions, two kinds of monitoring can be distinguished: off-line and on-line monitoring. Both kinds of monitoring as well as their influencing factors are discussed with on-site measurements on power transformers in service.

A machine condition transfer function approach to run-to-run and machine-to-machine reproducibility of III-V compound semiconductor molecular beam epitaxial growth

A concept of machine condition transfer function (MCTF) based on the use of in-situ sensor response to intrinsic surface property of the material is proposed to meet the challenge of run-to-run and machine-to-machine reproducibility of optimized growth conditions for III-V compound semiconductor molecular beam epitaxical growth. The variation in the intensity of the specular beam in reflection high-energy electron diffraction from compound semiconductor surface, measured as a function of the temperature and anion pressure prior to growth, is used as the intrinsic surface property for the generation of MCTF's. The mathematical methodology for realizing MCTF's, including the sensor response surface reconstruction and optimal minimization in combination with a composite statistical design for initial estimation, is presented. Numerical evaluation of the developed methodology shows its promise in practice.

電気化学インピーダンススペクトロスコピー (EIS) の理論と解析の基礎

Electrochemical Impedance Spectroscopy (EIS) has been known as a powerful tool for analyzing electrode reaction mechanism. In this review the history of EIS, the definition of electrochemical impedance, the general concept of transfer function, and the measurement method of electrochemical impedance using a transfer function analyzer are first introduced. Then, analytical methods of impedance spectra using electrical equivalent circuits and the kinetic theory of electrochemical reactions are stated. Finally, the future scope of EIS is briefly given.

Direct Robust Sampled-Data Marine Control Systems Design on Basis of Parametric Transfer Function Method

The problem of robust digital control of a continuous-time plant is addressed. A novel method is proposed for the direct design of robust digital controllers, that provides for stability and high-quality plant stabilization under non-parametric perturbations in the plant and disturbance models. The method is based upon the parametric transfer function concept. A polynomial-based algorithm is presented for designing discrete transfer function of the optimal robust controller.

Frequency Effects on Dynamic Stability Derivatives Obtained from Small-Amplitude Oscillatory Testing

As a result of a continuing program of work to establish a basic understanding of the aerodynamic phenomena that ine uence agility, stability, and control of future combat aircraft cone gurations, it has become clear that the conventional stability or aerodynamic derivative model for the representation of aerodynamic loads in the aircraft equations of motion is no longer adequate. This paper discusses the limitations of the stability derivative model for modern combat aircraft maneuvers, in particular the problem of motion frequency effects in static and dynamic derivatives derived from small-amplitude oscillatory wind-tunnel tests, and presents an alternative modeling technique based on the concept of an aerodynamic transfer function. Nomenclature A = in-phase component of rolling moment response AR = amplitude ratio ai, bi, ci = constants in generalized transfer functions B = in-quadrature component of rolling moment response b = wingspan, m Cl = rolling moment coefe cient, L/qSb Clb,att = attached e ow component of steady-state derivative Clb,0

A Fourier rebinning algorithm incorporating spectral transfer efficiency for 3D PET

This paper presents a Fourier rebinning algorithm for three-dimensional image reconstruction in PET that incorporates the concept of spectral transfer function. It suggests the need for discarding low-frequency components in the rebinning. It also includes the correction for rebinning efficiency which was evaluated by simulations as a function of oblique angle of projections. The performance was optimized by high-pass filters and axial smoothing. The algorithm yields satisfactory images with negligible axial cross-talk for a maximum oblique angle up to . The statistical noise was evaluated in terms of `noise equivalent number of oblique angles', and reasonable results were obtained in view of the theoretical expectation. Ring artefacts due to noise are negligibly small.

A Behavioral Approach By Using Pencil Based System Models

Abstract In this article we consider the problem of analysis and design of linear time-invariant control systems by using the system models which are based on matrix pencils. Behaviors, poles, zeros, stability, controllability, observability, transfer function, and other traditional concepts are discussed mainly besed on the Willems’ behavioral approach. Moreover the extensions to LQ optimal control problem and computation of H norm are investigated.

Frequency-domain Method for [formula omitted]2 Optimization of Time-delayed Sampled-data Systems

A frequency domain method based on the parametric transfer function concept is developed for the design of digital control systems with time-delayed continuous-time plants. The method allows to investigate the behavior of sampled-data systems in continuous-time in terms of input-output relations. An algorithm is presented for the design of an optimal digital controller that minimizes a quadratic cost functional under stochastic disturbances. The method is applicable to the design of digital controllers for arbitrary linear continuous-time plants. © 1997 Elsevier Science Ltd.

Evolutionary Model of Viscoelastic Dampers for Structural Applications

The effects of temperature on the energy dissipation of viscoelastic dampers for seismic mitigation of structures are investigated. To simulate the damper behavior, an evolutionary model is proposed to describe the dependence of the mechanical properties of the damper on the deformation frequency and the temperature increase due to dissipation. Thermorheologically simple materials are considered and the influence of the deformation frequency on the storage and loss moduli is modeled using fractional derivative operators. The effect of material temperature on the force-deformation relation is modeled using the concept of evolutionary transfer function, and the proposed model is implemented using a step-by-step technique in the frequency domain. The predictions of the proposed model in the case of sinusoidal and seismic deformations show good agreement with experimental results. Finally, the response spectra of single-degree-of-freedom structures with added viscoelastic dampers and subjected to seismic excitation are computed using the proposed evolutionary model; the results obtained show that the thermal effect due to energy dissipation is not always negligible.

Influence of aperture diameter on image contrast and resolution in scanning near-field optical microscopy

The influence of aperture diameter on image contrast and resolution in scanning near-field optical microscopy has been investigated. Evanescent standing wave fields at glass–air interfaces were probed with well-characterized aluminum-coated fiber tips. A strong decrease in image contrast was found when the aperture diameter exceeds a critical value. Numerical simulations with the concept of an intensity transfer function using the axial component of the Poynting vector inside the probe demonstrate that this phenomenon is the result of the increasing influence of higher-order waveguide modes on power transmission through the probe. It has been shown that standing wave patterns are convenient and reliable reference devices for individual probe characterization and quantification of their resolving power.

Two-dimensional numerical simulation of the photon scanning tunneling microscope. Concept of transfer function

A numerical simulation is used to calculate the signal detected by a photon scanning tunneling microscope when scanning a surface. We show that the signal provides an image very different from the actual surface profile. However, it is possible to define a transfer function relating the signal and the near-field intensity which exists without the presence of the detecting probe tip. Such a transfer function cannot be defined between the signal and the surface.

Three-dimensional Image Formation in Confocal Microscopy Under Ultra-short-laser-pulse Illumination

Reported in this paper is, to our knowledge, the first theoretical investigation of three-dimensional (3D) imaging properties in a confocal microscope under ultra-short-pulse illumination. Time-resolved, time-averaged and interferometric imaging modes in reflection and transmission systems are considered. The concept of the 3D transfer function is used to understand the imaging performance of the system. In the case of a 10fs pulse, the spatial frequency bandwidth in the axial direction is twice that for a system under continuous-wave (CW) illumination, while the spatial frequency bandwidth in the transverse direction is increased by only 10%. As a result, axial resolution can be improved by approximately 30%, compared with the limiting value under CW laser illumination of the same wavelength as the pulsed beam.

On local and global sigma-pi neural networks a common link

In general, there is a great difference between usual three-layer feedforward neural networks with local basis functions in the hidden processing elements and those with standard sigmoidal transfer functions (in the following often called global basis functions). The reason for this difference in nature can be seen in the ridge-type arguments which are commonly used. It is the aim of this paper to show that the situation completely changes when instead of ridge-type arguments were so-called hyperbolic-type arguments. In detail, we show that usual sigmoidal transfer functions evaluated at hyperbolic-type arguments—usually called sigma—pi units—can be used to construct local basis functions which vanish at infinity and, moreover, are integrable and give rise to a partition of unity, both in Cauchy's principal value sense. At this point, standard strategies for approximation with local basis functions can be used without giving up the concept of non-local sigmoidal transfer functions.

Microwave backscatter from the sea: Modulation of received power and Doppler bandwidth by long waves

Two continuous wave microwave systems were mounted on an elevator on the German Forschungsplattform Nordsee (FPN) during the Synthetic Aperture and X Band Ocean Nonlinearities (SAXON)‐FPN experiment. Here we report on measurements of long‐wave effects in the power received by these systems and in the Doppler bandwidths recorded from the systems. The two systems operated at X and Ka bands (10 and 35 GHz) and collected HH‐ and VV‐polarized backscatter signals simultaneously. The elevator system allowed us to vary the altitude of the microwave antennas above the sea surface from 7.5 to 27 m, always in the far field of the antennas. Most data were collected at a 45° incidence angle, which implied that the Ka band system illuminated areas from 0.4 to 6.0 m2 while the X band system viewed spots between 2.9 and 41.3 m2. We have attempted to characterize the modulation of both received power and Doppler bandwidth in terms of the standard modulation transfer function (MTF) concept. We find that our measurements of the MTF for received power agree well with previous measurements at X band but that the phase of the MTF for VV polarization is different from that previously reported for Ka band at a 60° incidence angle. We show how the amplitude and phase of the MTF as well as the coherence function vary with wind speed, long‐wave frequency, long‐wave propagation direction, and antenna height. In the case of the first three parameters our results agree with previous work except as noted above for Ka band. The dependence of the MTF on antenna height has not been investigated previously. Our results show that this dependence is small and well explained by the height variations induced as long waves propagate through the footprint on the surface. When we apply the MTF concept to the Doppler bandwidth, we find that the MTF of the bandwidth is small except at very low wind speeds. In view of the association of this bandwidth with velocities of subresolution‐scale, or intermediate‐scale, waves which are themselves modulated by the long waves, we find these small MTFs associated with Doppler bandwidths to be somewhat surprising. We present a simple model to attempt to draw inferences about the amplitude modulation of intermediate‐scale waves from our results. We also conclude from the small MTFs for Doppler bandwidths that the assumption of a constant correlation time in theories of synthetic aperture radar imagery of the ocean is well justified.

Spectrum Characteristics and Transfer Function of the Hydrograph of the Deep Aqueous System1

Abstract The fluctuation of most of the hydrograph in the deep aqueous system records the fluid pulsation in lithosphere and variation of the earth's crust. Many observations have verified that groundwater is an ideal information carrier of the crust. In this paper, the series of input (precipitation, air pressure, Earth tide etc.) and output (water level, artesian flow) of the deep aqueous system are studied by using the spectrum analysis and system theory. The application concepts of transfer function and the spectral structure of the hydrograph enrich the knowledge of the deep aqueous system. Two typical spectral structures of the hydrograph of the deep aqueous system are obtained by comparing with many water—bearing systems of the Jizhong depression. One is from well Ma—17 and the other is from the well Xinze—5. Finally, the physical models of forming the spectrum of the hydrograph are constructed on the basis of the spectrum research on the deep aqueous system.