Individual Transfer Functions Research Articles

Boundary element method calculation of individual head-related transfer function. II. Impedance effects and comparisons to real measurements.

Following previous work by the author involving the calculation of an individual head-related transfer function (HRTF) using a Boundary Element Method (BEM) approach, impedance conditions are now included to take account of the acoustic properties of human hair. In addition, comparisons are made here between calculations and measured values for the HRTF of a specific individual. Numerous works have been published regarding the measurement of HRTFs, but rarely are several methods compared for the same individual. The results presented in the work compare two different measurement techniques and a computational BEM for acquiring an individual HRTF. Impedance effects have been incorporated in the BEM model for hair based on measured data, providing a final set for comparison. Measurement results show significant variations for the same individual. Computational results show good agreement within the range of experimental variations. Definite trends are observed for many directions, while the limitations of the methods are also highlighted for others. The effects of incorporating hair impedance are shown to provide an improvement in the correlation of computational results, indicating an affect of hair impedance on the HRTF.

Boundary element method calculation of individual head-related transfer function. I. Rigid model calculation.

Human spatial perception of sound is a complex phenomenon. The Head-Related Transfer Function (HRTF) is a vital component to spatial sound perception. In order improve the understanding of the correlation between the HRTF and specific geometry of the head and pinna, a Boundary Element Method (BEM) has been used to calculate a portion of the HRTF of an individual based on precise geometrical data. Advantages of this approach include the ability to alter the geometry of the individual through the model in ways which are not possible with real subjects. Several models are used in the study, including a head with no pinna and several sized spheres. Calculations are performed for various source locations around the head. Results are presented for rigid model cases. Effects of variations on impedance and comparisons to measured data will be presented in the subsequent paper.

Transfer functions as a basis for the verification of models – variability and restraints

Objective. The seat-to-head transfer function of the human body reflects the biodynamic response. Based on measured data, biodynamic models have been proposed to reflect this response. They must satisfy usually the international published mean values of the seat-to-head transfer function. The question arises to what extent mean values reflect individual pattern of biodynamics. Methods. An experimental study was performed with 39 male subjects sitting on a hard seat without back rest and with supported feet. They were exposed to random whole-body vibration at three intensities with a relaxed and an erect posture. The accelerations in the z-direction were measured at the seat and head. The seat-to-head transfer functions with the associated coherence functions were calculated. Results. The biodynamic response characterised by the maximum of the seat-to-head transmissibility and the frequency of its occurrence is influenced by the posture of the subjects in a dominant way and shows an individual variability of considerable extent. The mean responses suggest a missing effect of vibration intensity, but individually different effects of the intensity were found. Repeated measurements confirmed this result. Conclusions. The application of a model validated by the comparison with mean values of the transmissibility could cause misleading conclusions, if it is used for the prediction of individual spinal loads. Models prepared for the calculation of individual loads should be validated by a mean individual transmissibility derived from repeated measurements. Relevance The results illustrate the loss of information by averaging individual transfer functions and the consequence of a limited validity and applicability in occupational health, ergonomics, and design.

Computational model of an individual head-related transfer function using the BEM

The head-related transfer function (HRTF), determined by the complex geometry of the pinnae and head, is the primary research and commercial tool for exploring and exploiting 3-D auralization and auditory localization. Research into the determining characteristics of the HRTF is difficult, as the anatomical variations between individuals are many. These variations make comparisons between individuals less than ideal for determining the relation between structure of the individual and components of the HRTF. This paper will discuss an investigation into the use of a geometrical model of an individual to calculate the HRTF. The calculation utilizes the boundary element method (BEM). As a tool, the use of a computer model allows for selected variations in the individual’s anatomy and direct observation of the results, a difficult task in experimental measures. Previous work by the author discussed the variability in experimental measurement techniques of the HRTF. Comparisons are made between the model results and these HRTF measurements for the same individual. Some preliminary variations to the model and their effects are also discussed. Computational results show good agreement with the general trends of the measurements and the frequency limitations of the computation. a)Currently at Artec Consultants, Inc., 114 W. 26th St., New York, NY 10001.

Blind System Identification Using Normalized Fourier Coefficient Gradient Vectors Obtained from Time-Frequency Entropy-Based Blind Clustering of Data Wavelets

A method for the blind identification of spatially varying transfer functions found in various remote sensing applications such as medical imagery, radar, sonar, and seismology is described. The techniques proposed herein are based on model matching of Fourier coefficient sensitivity vectors of a known transfer function, which can be nonlinear in the parameters, with a set of eigenvectors obtained from data covariance matrices. One distinction between this technique and usual channel subspace methods is that no FIR structure for the individual transfer functions is assumed. Instead we assume that the frequency response as a function of the parameters is known as is often the case in wave transmission problems. A channel identification procedure based on subspace matching is proposed. The procedure matches the eigenvectors of the signal deviation covariance matrix to a set of scaled and energy-normalized sensitivity vectors. For the case where neither the number of channels, the model parameters of each channel nor the membership assignment of data traces to the channels is known, we propose a novel preliminary clustering process. By separating the data into clusters of modest variability such that the measurements are linear with the parameters, we are able to deduce all of the above. The clustering is based on feature vectors obtained from a time-frequency entropy measure, also a novelty of our paper. To support the theory developed, we include parameter estimation results based on simulated data backscattered from a synthetic multi-layer structure.

Estimation of central aortic pressure waveform by mathematical transformation of radial tonometry pressure. Validation of generalized transfer function.

Central aortic pressures and waveform convey important information about cardiovascular status, but direct measurements are invasive. Peripheral pressures can be measured noninvasively, and although they often differ substantially from central pressures, they may be mathematically transformed to approximate the latter. We tested this approach, examining intersubject and intrasubject variability and the validity of using a single averaged transformation, which would enhance its applicability. Invasive central aortic pressure by micromanometer and radial pressure by automated tonometry were measured in 20 patients at steady state and during hemodynamic transients (Valsalva maneuver, abdominal compression, nitroglycerin, or vena caval obstruction). For each patient, transfer functions (TFs) between aortic and radial pressures were calculated by parametric model and results averaged to yield individual TFs. A generalized TF was the average of individual functions. TFs varied among patients, with coefficients of variation for peak amplitude and frequency at peak amplitude of 24.9% and 16.9%, respectively. Intrapatient TF variance with altered loading (> 20% variation in peak amplitude) was observed in 28.5% of patients. Despite this, the generalized TF estimated central arterial pressures to < or = 0.2 +/- 3.8 mm Hg error, arterial compliance to 6 +/- 7% accuracy, and augmentation index to within -7% points (30 +/- 45% accuracy). Individual TFs were only marginally superior to the generalized TF for reconstructing central pressures. Central aortic pressures can be accurately estimated from radial tonometry with the use of a generalized TF. The reconstructed waveform can provide arterial compliance estimates but may underestimate the augmentation index because the latter requires greater fidelity reproduction of the wave contour.

Approximate Dynamic Models for Recycle Systems

There has been recent interest in the dynamics and control of plants with recycle, due particularly to the complex dynamics that these plants can exhibit. While the transfer functions for the recycle system may be constructed from the individual linear transfer functions for each of the subunits comprising the plant, the resultant overall plant transfer function will often contain denominator deadtime terms. These denominator deadtime terms preclude the use of time-domain simulations and most of the common advanced controller design algorithms as the mathematical methods employed by these techniques require transfer functions with rational denominators. It is therefore necessary to simplify these models before they can be used, and the purpose of this paper is to present a technique suitable for these model simplifications which retains the original system stability and has a strong intuitive appeal.

Magnetostrictive amorphous sensor for the detection of human respiration

A simple sensor for the detection of respiratory and cardiac activity is based on changes in the circumference of the human thorax. The sensor consists of magnetostrictive amorphous ribbons glued to the convex side of a prebent nonmagnetic layer. As a result, elongation is transferred into compressive stress, which reduces the ribbon's permeability, and a proportional voltage signal, respectively. The paper discusses major practical problems which result from the material's nonlinear behaviour, the sensor's individual transfer function, its undefined pre-stress and the elasticity of the applied sensor belt. In an effective way, overall linearization can be attained by means of wide-range calibration functions stored in a computer file. Alternatively, scaling by means of a spirometer yields quantitative evaluations, but restricted to respiration.

M-Input m-output feedback control by individual channel design Part 1. Structural issues

A new applications-oriented approach—individual channel design (ICD)—to multivariable feedback control for 2-input 2-output systems was presented and justified in a series of papers (O'Reilly and Leithead 1991, Leithead and O'Reilly 1991 a, b, 1992 a). This paper is the first part of a two-part investigation into the extension of the ICD framework, and the performance issues thereof, to general m-input m-output systems. The main results of this first part are fourfold. First, the ICD framework for general m-input m-output systems is justified for all multivariable system structures (RHP poles and zeros). In particular, it is shown that ICD on the original m-input m-output cross-coupled multivariable system is valid irrespective of the degree of cross-coupling. Second, the influence of (individual transfer function, channel, transmission) right half-plane zeros on controller design and closed-loop channel performance is elucidated. Third, the existence of fixed stabilizing controllers for uncertain m-input...

Multiple source auralization progress report

The problem of accurate spatial representation of large orchestras in binaural auralizations is attacked by convolving anechoic recordings of individual instruments with the room impulse responses simulated from each instrument location to a single listener location and subsequently mixed. Instrument directivity and power, orchestra member effects, individual pinna transfer functions, and headphone transfer functions are considered. Progress, techniques, limitations, and problems of this current research will be discussed. [Research supported by The Talaske Group, Inc.]

Controllability Analysis for Unstable Processes

We study the controllability of unstable processes, with emphasis on selection of measurements and manipulated variables, and the pairing, problem for dessatralized control. The well known pairing criteria based on the Niederlinski Index and the steady state Relative Gain Array (RGA) have been generalized to open loop unstable plants. Right Half Plane (RHP) zeros in individual transfer func-tion dements may make it practically impossible to stabilize the individual loops, and in such cases these pairing criteria are not very helpful. We have found RGA ≈ I in the bandwidth region to indicate good pairings also when paired elements have significant RHP zeros, but have found the Direct Nyquist Array (DNA) to perform poorly as an indicator of good pairings. In some cases it is preferable to avoid pairings giving narrow Gershgorin bands.

A Simplified Multi-Input Multi-Output Formulation for the Quantitative Feedback Theory

A simplified multi input/output formulation is developed for the quantitative feedback theory (QFT) for the 2 × 2 (n = 2) case. This formulation is consistent with traditional QFT philosophy where performance is specified for each individual closed-loop transfer function and control bandwidths are minimized. The simplified formulation turns the solution of a simultaneous robust stability and robust model matching problem into a two (n in general) step procedure of solving quadratic inequalities (whose coefficients are linear functions of the plants and the performance constraints); the traditional procedure requires six (n + n2 in general) steps for a similar problem. A numerical example illustrates the simplified formulation and demonstrates its ability to offer useful insight in a control design.

Evaluating estimation of gain directionality

The analysis method presented in part 1 of this paper is applied to case studies of binary distillation using the LV and DV control configurations. Based on this we conclude that insufficient estimation of the maximum and minimum process gains for multivariable systems, i.e. gain directionality, is caused by misalignment of inputs and outputs with the corresponding input and output singular vectors, together with a high condition number. This uncertainty has a significant impact on the achievable control performance of multivariable controllers designed from the identified model. For these classes of MIMO systems we show that the uncertainty in the estimate of gain directionality can be reduced by using multi-input perturbations or preferably closed-loop identification as opposed to single-input perturbations. In the case of closed-loop identification it is sufficient to use simple single-loop proportional control, designed from limited qualitative knowledge about the plant. For standard parametric identification commonly used model evaluation techniques, such as degrees of explanation and the quality of the estimated individual transfer functions, are compared to the methodology presented in part 1. As shown, these standard evaluation techniques cannot be used to conclude whether the gain directionality has been adequately estimated. However, using the proposed method tight bounds are obtained on the quality of the estimated gain directionality. Furthermore, we illustrate that the quality of the estimate of gain directionality has a strong impact on achievable control performance, i.e. a significant error in the estimate of the low-gain direction in the plant will cause significant deterioration of the control performance whenever control action is required in this direction. Thus, by using proper scaling of the plant inputs and outputs the method presented analyses the model quality with respect to the control problem at hand.

A Direct Adaptive Controller for Non-minimum Phase Multivariable Systems with Arbitrary Time Delays

A direct adaptive multivariable control scheme based on the ideas of model reference adaptive controllers is presented, which is applicable to minimum and a certain class of non-minimum phase systems. The general time delay case is considered, where the individual transfer functions of the multivariable system may have different arbitrary time delays. In order to stabalize nonminimum-phase adaptive control and to weight the control cost, the plant output vector is augmented by filtered plant input signals. Adaptive feedforward control is included to compensate measurable load changes or other disturbances. A new estimation algorithm is introduced, which is related to "fixed gain" ana stochastic approximation techniques.

An input-output characterization for linearization by feedback

For a stationary, initially-relaxed, single-input, single-output, bilinear-realizable system that is described by a sequence of regular transfer functions, the relative degrees of the individual transfer functions are defined in a manner similar to the linear case. These relative degrees are used to characterize the region where linear input-output behavior can be obtained by state feedback in a bilinear realization of the system.

Transmission bandwidth of the two-mode fiber link

The transmission bandwidth of the two-mode fiber link is investigated both experimentally and theoretically. It is shown that the experimental bandwidth as a function of wavelength is accurately predicted by using the individual fiber transfer functions and the mode conversion matrix at a splice. The bandwidth is maximized at the wavelength where the overall group delay time difference between the LP 01 and LP 11 modes becomes zero, showing the so-called modal equalization effect. It is experimentally certified that the 3 dB bandwidth over 2 GHz is obtained in the wide two-mode-propagation spectral region around 1.3 μm for 5.2 km long two-mode fiber link for the maximum output power launching condition, due to the relatively large attenuation of the LP 11 mode after long propagation.

Comment on "Parameter and structural identifiability concepts and ambiguities: a critical review and analysis".

Identifiability of a model for the glucose tolerance test, considered by Cobelli and DiStefano [Am. J. Physiol. 239 (Regulatory Integrative Comp. Physiol. 8): R7-R24, 1980], is shown to depend on the shape of the external perturbation. For systems with two or more inputs applied simultaneously, it is essential in Laplace transform identifiability analysis to examine the Laplace transform(s) of the observation(s) rather than the individual transfer functions, which are not measurable separately.

Identification of Multi-Input Multi-Output Linear Systems From Frequency Response Data

A procedure for identifying a multi-input multi-output linear system from frequency response data is developed. Individual transfer functions from individual input to individual output are identified via the generalized least-squares theory. Orders of the transfer functions are determined by testing the residual. The minimal order multi-input multi-output system is identified based on the formation of a composite system comprising the subsystems associated with all individual outputs followed by decomposition. This is actually the problem of minimal realization involving inexact system parameters.

Electro-optic processing in longwave holography

This paper presents an attempt to link the complex and semi-empirical parameters of longwave holography in a way which allows the reader to survey the total problem and optimise the experimental regime. The individual and composite transfer functions of the CRT and the two-step photographic recording are discussed and examined. Requirements for the electronic amplifier that compensates for the non-linearity of these three components and which allows the linearisation of the entire process are discussed. Dynamic range and linearity test are proposed.

Characterization and spectral equalization for hight-density disk recording

For a 3350 type head/disk interface, the amplitude spectrum of an experimental characteristic pulse deviates slightly from the idealized Lorentzian distribution in the signal bandwidth; but the phase spectrum of the experimental pulse is quite distorted from the desired linear phase, causing the widely observed asymmetrical time-domain waveform. A quantitative characterization and comparison are presented and individual transfer functions for ideal linear equalization are proposed. To remove the intersymbol interference, i.e., the linear portion of the distortion, from the playback signal of a high-density system, several cosine-power-law spectral candidates, with minimized noise enhancement and the capability of restoring amplitude loss and timing error, are explored. A unified relationship for the entire family of cosine-power-law spectral shapes and their bandwidth tradeoffs are identified, allowing for optimum read equalization at a tolerable signal-to-noise penalty. This is a useful tool for exploring practical density limitations of any given head/disk interface.