Calculation Of Transfer Function Research Articles

Calculation of transfer function of acoustic feedback path for in-the-ear hearing aids with a correction for specific acoustic impedance of a tubule

Calculation of transfer function of acoustic feedback path for in-the-ear hearing aids with a correction for specific acoustic impedance of a tubule

Optimal sample length for calculating transfer functions from discrete experimental data

Transfer functions are useful tools in observing the behaviour of non-linear systems. Transfer functions convert an input signal into an output signal, and for non-linear systems can be calculated separately for each order of response using the Volterra series. The Volterra series quantifies the linear and non-linear responses separately for systems with either Gaussian or non-Gaussian inputs, and is particularly useful when calculating transfer functions from experimental data, as the calculations can be performed using a discrete frequency domain format. The application of the Volterra series to discrete experimental data requires careful consideration of various factors that impact on the successful calculation of transfer functions. The single largest problem faced when using discrete experimental data is the difficultly presented when determining the optimal sample length of the data adopted during the calculation process. Equal lengths of sample data are extracted from each individual record to calculate averaged input and output spectra. When using experimental data of finite record length, a trade off between the number of sample lengths obtained from each record and the frequency interval of the resulting transfer functions occurs. Here we explore those factors that lead to the selection of an optimal sample length. We begin with an overview of the Volterra series approach, and how experimental data can be used to calculate transfer functions. The factors that influence the selection of the optimal sample length are described and methods outlined that ensure the most meaningful results are obtained. We demonstrate these methods using the results from an experimental procedure performed on a model Tension Leg Platform.

Computation of dynamic characteristics of control systems: An Effectiveness enhancement method

The Simoy method of computation of transfer functions from transition curves is modified and improved such that selection of an optimal structure for a transfer function from synthesized variants for the channel of action of an element and computation of its parameters are implemented sequentially and automatically, and then the optimal values of computed parameters of transfer functions are determined by minimizing the approximation error. This method enhances the accuracy of computation of dynamic characteristics at least by 20%.

Transfer Function Calculations for Aeroengine Combustion Oscillations

Combustors with fuel-spray atomizers are particularly susceptible to a low-frequency oscillation at idle and subidle conditions. For aeroengine combustors, the frequency of this oscillation is typically in the range 50–120 Hz and is commonly called “rumble.” The mechanism involves interaction between the plenum around the burner and the combustion chamber. Pressure variations in the plenum or the combustor alter the inlet air and fuel spray characteristics, thereby changing the rate of combustion. This in turn leads to local “hot spots” which generate pressure oscillations as they convect through the downstream nozzle. In order to eliminate the combustion oscillations, it is essential to determine which fuel atomizers are particularly likely to lead to instability by quantifying their sensitivity to flow perturbations. This can be done by identifying the system through understanding the transfer function, which represents the relationship between the unsteadiness of combustion and the inlet fuel and air. In the present work, various types of signals are applied to produce a small change in the inlet fuel and air flow rates, the response in the rate of heat release caused downstream was calculated and stored for subsequent analysis. Afterwards, the system transfer function is calculated by determining the coefficients of an IIR filter (Infinite Impulse Response) for which the output signal is the downstream heat release rate and the input signal is the inlet flow rate. The required transfer function then follows from the Fourier transform of this relationship. The resulting transfer functions are compared with those obtained by the forced harmonic oscillations at a fixed given frequency. Suitably chosen input signals accurately recover the results for harmonic forcing at a single frequency, but also give detailed information about the combustor response over a wide frequency range. There are two distinct forms to the low-frequency quasisteady response. In the primary zone, the rate of combustion is influenced by the turbulence and is enhanced when the inlet air velocity is large. Near the edge of combustion zone, the rate of combustion depends on the mixture fraction and is high when the mixture fraction is close to the stoichiometric value. This generates ‘hot spots’ which convect into the dilution zone. At higher frequencies, the combustion lags this quasi-steady response through simple lag-laws and the relevant time delays have been identified.

Real time computation and temporal coherence of opacity transfer functions for direct volume rendering of ultrasound data

Opacity transfer function (OTF) generation for direct volume rendering of medical image data is an intensely discussed subject. Several automatic methods exist for CT and MRI data, which are not apt for ultrasound data, mainly due to its low signal-to-noise ratio. Furthermore, ultrasound (US) imaging is able to produce time-varying 3D datasets in real time thus opening the door to 4D visualization. However, OTF design for 4D datasets has not been exhaustively discussed until now. We present an efficient solution to generate an optimized OTF for a given 3DUS dataset in real time. Our method results in excellent visualization which we demonstrate using 3D fetus datasets. Finally, we discuss the applicability of our method to 4DUS visualization.

Reduced-Complexity Error-State Diagrams in TCM and ISI Channel Performance Evaluation

The performance evaluation of trellis-coded modulation (TCM) schemes and intersymbol interference (ISI) channels via union bounds involves a transfer function computation of an error-state diagram which enumerates all possible error events. This letter presents a new method for obtaining equivalent error-state diagrams with a reduced number of states.

A new software suite for NO 2 vertical profile retrieval from ground-based zenith-sky spectrometers

Here we present an operational method to improve accuracy and information content of ground-based measurements of stratospheric NO 2. The motive is to improve the investigation of trends in NO 2, and is important because the current trend in NO 2 appears to contradict the trend in its source, suggesting that the stratospheric circulation has changed. To do so, a new software package for retrieving NO 2 vertical profiles from slant columns measured by zenith-sky spectrometers has been created. It uses a Rodgers optimal linear inverse method coupled with a radiative transfer model for calculations of transfer functions between profiles and columns, and a chemical box model for taking into account the NO 2 variations during twilight and during the day. Each model has parameters that vary according to season and location. Forerunners of each model have been previously validated. The scheme maps random errors in the measurements and systematic errors in the models and their parameters on to the retrieved profiles. Initialisation for models is derived from well-established climatologies. The software has been tested by comparing retrieved profiles to simultaneous balloon-borne profiles at mid-latitudes in spring.

Eye models for the prediction of contrast vision in patients with new intraocular lens designs.

Theoretical calculations of the polychromatic modulation transfer function (MTF) and wave-front aberration were performed with physiological eye models. These eye models have an amount of spherical aberration that is representative of a normal population of pseudophakic eyes implanted with two different types of intraocular lens (IOL) made from high-refractive-index silicone. These theoretical calculations were compared with the measured contrast sensitivity function (CSF) under mesopic lighting conditions and with wave-front aberration (obtained with a Hartmann-Shack wave-front sensor) collected from 37 patients bilaterally implanted with the same types of lens. The relationships between the ocular wave-front aberration and the MTF predicted by the eye models and the CSF and the ocular wave-front aberration measured in eyes implanted with IOLs were investigated. The predicted improvements in MTF and wave-front aberration correlated well with the improvements measured in practice. Physiological eye models are therefore useful tools for IOL design.

Focal plane array infrared camera transfer function calculation and image restoration

Infrared images often present distortions induced by the measurement system. Image processing is thus an essential part of infrared measurements. A distortion model based on a convolution product is presented. The analytical form of the convolution kernel has been obtained from an image formation theory, along with an analysis of the sampling of the focal plane array camera detector's matrix. Image restoration is an ill-posed problem, and its solution can be obtained using regularization methods. In this work, image restoration is performed using a variation of Tikhonov regularization that makes use of the particular form of the convolution kernel matrix, which is built as a block-circulant matrix that admits a diagonal form in the 2-D Fourier space. The restoration procedure is used to restore a knife-edge infrared source image.

Use of Vertical Wave Bending Moments From Hydrodynamic Analysis In Design of Oil Tankers

SUMMARY The paper describes calculation of design vertical wave bending moments for unconventional oil product tankers of new generation that are characterized by low length-to-beam ratio. The linear strip theory is employed for the calculation of transfer functions, while standard IACS procedure is used for long-term prediction of extreme values. Since the calculated design vertical wave bending moments at midship largely overestimate the values from IACS UR S11, additional analyses are performed to explain these differences. For that purpose, the same analysis is performed for conventional oil tanker which fully complies with contemporary IACS rules. Large overestimations of rule vertical wave bending moments are obtained also for that ship. The inaccuracies of the linear strip theory may partially explain these overestimations, as discussed in the paper. The wave scatter diagram proposed by IACS is analysed and found to be too severe for strength analysis of ship structures. However, the severity of the IACS scatter diagram is compensated by some other unconservative assumptions in the standard long-term prediction procedure, which is also elaborated. After all these aspects are put together, the obvious conclusion is that the IACS rule vertical wave bending moment should be substantially increased to enable safe design of oil tankers navigating in the North Atlantic wave climate. Finally, some suggestions regarding incorporation of hydrodynamic analysis for the calculation of extreme wave loads in ship design are given.

Premixed Flame Kinematics in a Longitudinal Acoustic Field

response to velocity perturbations. The transfer function relating e ame area e uctuations to acoustic velocity perturbations is calculated numerically and compared with analytical, one-dimensional results. In addition to the Strouhal number, these more general results depend upon the temperature ratio across the e ame, the diameter ratio of the rapid expansion, and the ratio of e ame length to duct diameter. It is shown that the e ame transfer function is qualitatively similar in many cases, however, and that the Strouhal number remains the dominant parameter affecting the calculated transfer function. Analysis reveals that thedifferencesbetween the two calculations arise from gas compressibility in the e ame region and spatial nonuniformity (not two-dimensionality) in the acoustic velocity along the e ame front. These results clarify the reasons behind the rather unexpected agreement between the simplie ed one-dimensional theory and the measurements of Ducruix et al. (Ducruix, S., Durox, D., and Candel, S., “ Theoretical and Experimental Determinations of the Transfer Function of a Laminar Premixed Flame,” Proceedings of the Combustion Institute , Vol. 28, 2000).

Modeling and simulation of next-generation multimode fiber links

This paper describes an advanced multimode-fiber-link model that was used to aid the development of Telecommunication Industry Association standard specifications for a next-generation 50-μm-core laser-optimized multimode fiber. The multimode-link model takes into account the interactions of the laser, the transmitter optical subassembly, and the fiber, as well as effects of connections and the receiver preamplifier. We present models for each of these components. Based on these models, we also develop an efficient and simple formalism for the calculation of the fiber transfer function and the signal at the link output in any link configuration. We demonstrate how the model may be used to develop specifications on transmitters and fibers that guarantee any desired level of performance.

Finite difference computation of head-related transfer function for human hearing.

Modeling the head-related transfer function (HRTF) is a key to many applications in spatial audio. To understand and predict the effects of head geometry and the surrounding environment on the HRTF, a three-dimensional finite-difference time domain model (3D FDTD) has been developed to simulate acoustic wave interaction with a human head. A perfectly matched layer (PML) is used to absorb outgoing waves at the truncated boundary of an unbounded medium. An external source is utilized to reduce the computational domain size through the scattered-field/total-field formulation. This numerical model has been validated by analytical solutions for a spherical head model. The 3D FDTD code is then used as a computational tool to predict the HRTF for various scenarios. In particular, a simplified spherical head model is compared to a realistic head model up to about 7 kHz. The HRTF is also computed for a realistic head model in the presence of a wall. It is demonstrated that this 3D FDTD model can be a useful tool for spatial audio applications.

Efficient acoustic calculations by the BEM and frequency interpolated transfer functions

Following the demand for more economic and faster algorithms in computational acoustics, a new procedure is developed, which allows the calculation of frequency dependent acoustic transfer functions in a very efficient way. It is based on an indirect boundary element method which is combined with a special source simulation technique. The combination allows a rather accurate and systematic approximation of acoustical results in major parts of the considered frequency range. This leads to a significant reduction of the computer time needed to calculate complete frequency spectra. Two basic examples are shown which demonstrate how the new approach can be used. The procedure turns out to be computationally very powerful and it seems to be a very promising step towards a more efficient calculation of complex sound radiation problems.

Analysis of a non-linear structure by considering two non-linear formulations

In recent years, modal synthesis methods have been extended for solving non-linear dynamic problems subjected to harmonic excitation. These methods are based on the notion of non-linear or linearized modes and exploited in the case of structures affected by localized non-linearity. Actually, the experimental tests executed on non-linear structures are time consuming, particularly when repeated experimental tests are needed. It is often preferable to consider new non-linear methods with a view to decrease significantly the number of attempts during prototype tests and improving the accuracy of the dynamic behaviour. This article describes two fundamental non-linear formulations based on two different strategies. The first formulation exploits the eigensolutions of the associated linear system and the dynamics characteristics of each localized non-linearity. The second formulation is based on the exploitation of the linearized eigensolutions obtained using an iterative process. This article contains a numerical and an experimental study which examines the non-linear behaviour of the structure affected by localized non-linearities. The study is intended to validate the numerical algorithm and to evaluate the problems arising from the introduction of non-linearities. The complex responses are evaluated using the iterative Newton–Raphson method and for a series of discrete frequencies. The theory has been applied to a bi-dimensional structure and consists of evaluating the harmonic responses obtained using the proposed formulations by comparing measured and calculated transfer functions.

Conditioning data for calculation of the modulation transfer function.

A method for conditioning data used in the measurement of the modulation transfer function (MTF) is discussed. This method is based upon imposing the constraint that the edge spread function (ESF) is monotonic. The advantages of this technique, when applicable, are demonstrated with simulated examples for which the true MTF is known. The application of this technique in the measurement of the MTF of a digital detector in clinical use is also demonstrated.

Influence of motion sensor error on image restoration from vibrations and motion

We investigate the influence of motion sensor errors on the calculation of a modulation transfer function (MTF) and its implementation in image restoration. The goal of this research is to describe an automatic system for restoration of pictures blurred by vibration, and to consider its possible disadvantages. We present an analytical approach for estimating the vibration MTF from the measured system MTF according to the frequency response of motion sensors and their noise data. Our method is based on point-spread function verification by the data of motion sensor characteristics. We build an analytical model of the sensor and analyze influences of errors caused by system noise and incorrect axis direction of the restoration device. Some image restoration of degraded images is presented based on improvements using the original wiener filter. Performances of inverse and wiener filter operations are compared, and the dependence of restoration quality on the signal-to-noise ratio and angle between the restoration axis and true vibration direction is considered. We also demonstrate the axis rotation sensitivity of the system, and describe improvements over the initial method as seen from our simulation. The key to the restoration is the determination of the improved modulation transfer function unique to the image vibration and sensor characteristics.

Calculation of vectorial three-dimensional transfer functions in large-angle focusing systems.

The optical transfer function (OTF) is used in describing imaging systems in the Fourier domain. So far the calculation of the OTF of a large-aperture imaging system has been difficult because the vectorial nature of light breaks the cylindrical symmetry of the pupil function. We derive a simple line integral solution for calculating the vectorial three-dimensional OTF. We further extend this approach to imaging through a planar interface of two media with mismatched refractive indices. In general, our formalism allows for calculation of the Fourier transform of any product of two arbitrary vector components of the electromagnetic field. Arbitrary phase or amplitude modifications of the pupil function can be taken into account.

CtfExplorer: Interactive Software for 1d and 2d Calculation and Visualization Of TEM Phase Contrast Transfer Function

ctfExplorer: Interactive Software for 1d and 2d Calculation and Visualization Of TEM Phase Contrast Transfer Function

A study on an estimation of inverse transfer function using an adaptive exponential filter

AbstractConsidering an adaptive system estimating the inverse of the transfer function (inverse transfer function) of an unknown system, a configuration is proposed in which the adaptive system is placed in front of the unknown system (pre‐inverse modeling). In general, when a transversal adaptive filter is used, the output delay signal of the unknown system is needed in the adaptive algorithm of the tap coefficient. This signal cannot be observed because an adaptive filter is inserted in the prior stage, so that a replica of the unknown system is needed. In this paper, an adaptive system that does not require this replica is considered. The inverse transfer function of the minimum‐phase section of the unknown system is estimated with an adaptive exponential filter by means of a gradient algorithm. Since the signal in the tap algorithm is the delayed output signal of the observable adaptive system, no replica is required. Convergence of the tap coefficients is rigorously studied theoretically from the point of view of monotonic increase of the gradient. Also, the minimum‐phase section of the unknown system is estimated with a transversal adaptive filter by using a gradient algorithm. A method of calculation of the inverse transfer function with this estimated value is presented. The algorithm of the two adaptive filters is a gradient algorithm that is easily realized with guaranteed convergence. Finally, numerical verification of the study results, performance evaluation of the adaptive system, and comparison with the conventional system are carried out by computer simulation. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(12): 47–55, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1127