Complex Frequency Response Research Articles

Design of linear time-domain filters for hearing protector modeling

Accurately modeling hearing protectors for predicting the hazard underneath them is of interest to many. This project modeled the single transfer path through the hearing protector from the free field to the ear drum, as an extension to the frequency-domain modeling method presented by Price and Kalb [J. Acoust. Soc. Am. 103, 2878 (1998)]. First, the real ear attenuation at threshold (REAT) data from the hearing protectors (muff and plugs) were converted to linear quantities and curve fit to form a continuous function of frequency, while preserving the low-pass characteristic. The resulting magnitude was combined with the head-related transfer function (HRTF) to form the magnitude of the total transfer function. Using complex cepstrum, a stable, complex frequency response function (FRF) was created by assuming a minimum phase transfer path. System identification methods were used to fit the FRF data to a parametric model that was converted to an infinite impulse response (IIR) digital filter. Subject-fit REAT data were used in order to represent real-world usage. Imperfect usage was modeled by derating the subject fit data by 1 standard deviation (SD). Tests on an artificial head are conducted to evaluate the filters in the time and frequency domains. [This research was supported wholly by NIOSH.]

Sonification of sound: Auditory display for acoustics education

Sonification is concerned with data representation to the ear using nonspeech audio. While auralization is routinely used in architectural acoustics, the broader processes encompassed by sonification are not so commonly applied, but can enhance the appreciation of acoustical properties of materials and structures, audio signals, and acoustic system measurements. We present examples of sonifications such as (i) auditory graphs of reflection and transmission coefficients and reverberation times; (ii) auditory graphs of percentiles and moments, applied to time‐varying sound levels and to magnitude spectra; (iii) conditioning of room impulse responses for sonification using techniques such as time stretching, signal reversal, filtering and auto‐convolution/correlation; (iv) sonification of complex frequency response or signal spectra; and (v) applications of the Hilbert transform for audio signal sonification. Compared to graphic or numeric representation, such sonifications have the advantage of providing an aural experience of the aspect of sound that is sonified, and so directly convey to a listener something of the meaning of the data.

Design of Real FIR Filters With Arbitrary Magnitude and Phase Specifications Using a Neural-Based Approach

An efficient and yet simple neural-based approach is utilized to design real finite-impulse response filters with arbitrary complex frequency responses in the least-squares sense. The proposed approach establishes the quadratic error difference of the filter optimization in the frequency domain as the Lyapunov energy function. Consequently, the optimal filter coefficients are obtained with good performance and fast convergence speed. To achieve good convergences for large filter lengths, a cooling process of simulated annealing is used for the neural activation function. Several examples and comparisons to the existing methods are presented to illustrate the effectiveness and flexibility of the neural-based method

Transfer Functions of One-Dimensional Distributed Parameter Systems by Wave Approach

An alternative analysis technique, which does not require eigensolutions as a priori, for the dynamic response solutions, in terms of the transfer function, of one-dimensional distributed parameter systems with arbitrary supporting conditions, is presented. The technique is based on the fact that the dynamic displacement of any point in a waveguide can be determined by superimposing the amplitudes of the wave components traveling along the waveguide, where the wave numbers of the constituent waves are defined in the Laplace domain instead of the frequency domain. The spatial amplitude variations of individual waves are represented by the field transfer matrix and the distortions of the wave amplitudes at point discontinuities due to constraints or boundaries are described by the wave reflection and transmission matrices. Combining these matrices in a progressive manner along the waveguide using the concepts of generalized wave reflection and transmission matrices leads to the exact transfer function of a complex distributed parameter system subjected to an externally applied force. The transient response solution can be obtained through the Laplace inversion using the fixed Talbot method. The exact frequency response solution, which includes infinite normal modes of the system, can be obtained in terms of the complex frequency response function from the system’s transfer function. This wave-based analysis technique is applicable to any one-dimensional viscoelastic structure (strings, axial rods, torsional bar, and beams), in particular systems with multiple point discontinuities such as viscoelastic supports, attached mass, and geometric/material property changes. In this paper, the proposed approach is applied to the flexural vibration analysis of a classical Euler–Bernoulli beam with multiple spans to demonstrate its systematic and recursive formulation technique.

Transient dynamic fracture analysis using scaled boundary finite element method: a frequency-domain approach

In the scaled boundary finite element method (SBFEM), the analytical nature of the solution in the radial direction allows accurate stress intensity factors (SIFs) to be determined directly from the definition, and hence no special crack-tip treatment, such as refining the crack-tip mesh or using singular elements (needed in the traditional finite element and boundary element methods), is necessary. In addition, anisotropic material behaviour may be handled with ease. These advantages are used in this study, in which a newly-developed Frobenius solution procedure in the frequency domain for solving the governing differential equations of the SBFEM, is applied to model transient dynamic fracture problems. The complex frequency–response functions are first computed using the Frobenius solution procedure. The dynamic stress intensity factors (DSIFs) are then extracted directly from the response functions. This is followed by a fast Fourier transform (FFT) of the transient load and a subsequent inverse FFT to obtain the time history of DSIFs. Benchmark problems with isotropic and anisotropic material behaviour are modelled using the developed frequency-domain approach. Excellent agreement is observed between the results of this study and those in published literature. The effects of the mesh density, the material internal damping coefficient, the maximum frequency and the frequency interval determining the frequency–response functions on the resultant accuracy and the computational cost are also discussed.

Dynamic response of a viscously damped cantilever with a viscous end condition

This paper deals with the dynamical analysis of a cantilevered Bernoulli–Euler beam subjected to distributed external viscous damping in-span and with a viscous end condition by a single damper. In order to evaluate the vibration characteristics of the system, a procedure is presented where overdamped and underdamped ‘‘modes’’ are investigated simultaneously, via the dynamic stiffness matrix of the system. Further, the orthogonality conditions, which allow the decoupling of the equations of motion in terms of principal coordinates, are derived. Then, the complex frequency response function is obtained through a formula which was established for the receptance matrix previously. Finally, the dynamic impulse response function of the system is evaluated in the time domain. Comparison with the numerical results obtained via a boundary value formulation justifies the approaches used here.

Measurement of the parameters of a pulse propagation path in a medium with noise, dispersion, and selective absorption

A method of signal processing is proposed that allows one to determine the propagation time of pulsed signals, the dispersion, and the selective absorption in the medium when the shape of the pulses is substantially distorted under the effect of the two aforementioned factors and noise. The method is based on measuring the complex frequency response of the propagation path for a narrow frequency band within which the frequency response is governed by the desired parameters of the medium. To determine the parameters of the path from the data of acoustic measurements, both cepstral analysis and numerical differentiation are used. The data of numerical experiments are presented.

Digital Laguerre filter design with maximum passband-to-stopband energy ratio subject to peak and Group delay constraints

In this paper, we formulate a general design of transversal filter structures with maximum relative passband-to-stopband energy ratio subject to complex frequency response constraints in the passband and the stopband as well as additional constraints such as null constraints. These null constraints are important for applications where the suppression of noise at certain frequencies are important. Additional constraints are introduced allowing approximately linear phase and constant group delay in the passband. For a given set of basis functions, the design problem can be formulated as a semi-infinite quadratic optimization problem in the filter coefficients, which are the decision variables to be optimized. In this paper, we focus on the design of digital Laguerre filter and digital finite impulse response (FIR) filter structures. A modified bridging algorithm is developed for searching for the optimum pole of the Laguerre filters. Design examples are given to demonstrate the effectiveness of the proposed algorithm.

Modulated photoluminescence studies for lifetime determination in amorphous-silicon passivated crystalline-silicon wafers

A simple, inexpensive method for characterization and quality control of silicon wafers and wafer coatings is proposed, based on the measurement of the complex frequency response of the photoluminescence signal to a sinusoidal excitation, which we term modulated photoluminescence. The minority carrier lifetime may be extracted directly from the phase information without the need for difficult and often imprecise intensity calibrations. We apply modulated photoluminescence measurements to study the influence of interface defects on the recombination of excess carriers in crystalline silicon wafers with different passivation schemes.

Vibroacoustical Damping Diagnostics: Complex Frequency Response Function versus its Magnitude

Vibroacoustical Damping Diagnostics: Complex Frequency Response Function versus its Magnitude

Relationship between Phase Shift, Square-Wave Response and Density of States in Modulated Photocurrent Spectroscopy

AbstractLow- and high-frequency modulated photoconductivity measurements (LF and HF MPC) have been made on amorphous silicon films prepared by the expanding thermal plasma (ETP) and RF PECVD techniques. Time constants have been measured by decay of square wave excitation and behavior of complex frequency response. The influence of quasi-Fermi level position has been examined. Band tail slopes of 32 meV (ETP) and 37 meV (PECVD), and defect densities of order 1018 and 1017 cm-3 eV-1 respectively are found. Tail state capture coefficients of order 3×10-8 cm3 s-1 are calculated from overlapping LF and HF regimes. Defect state values for ETP (< 10-8 cm3 s-1) are smaller than for PECVD silicon films (> 10-7 cm-3 s-1).

Sensitivity Analysis of Viscoelastic Structures

In the context of control of sound and vibration of mechanical systems, the use of viscoelastic materials has been regarded as a convenient strategy in many types of industrial applications. Numerical models based on finite element discretization have been frequently used in the analysis and design of complex structural systems incorporating viscoelastic materials. Such models must account for the typical dependence of the viscoelastic characteristics on operational and environmental parameters, such as frequency and temperature. In many applications, including optimal design and model updating, sensitivity analysis based on numerical models is a very usefull tool. In this paper, the formulation of first-order sensitivity analysis of complex frequency response functions is developed for plates treated with passive constraining damping layers, considering geometrical characteristics, such as the thicknesses of the multi-layer components, as design variables. Also, the sensitivity of the frequency response functions with respect to temperature is introduced. As an example, response derivatives are calculated for a three-layer sandwich plate and the results obtained are compared with first-order finite-difference approximations.

Application of frequency spectroscopy to fluorescence-based oxygen sensors

This study addresses the problem of specification of physical models for quenched-fluorescence-based oxygen sensors by analysing their complex frequency response (both intensity and phase signals) at different working frequencies and oxygen concentrations. Two common physical models of active medium, the single-exponential model with non-linear oxygen solubility and the double-exponential model were considered, with the example of heterogeneous PtOEPK-PS-based oxygen sensor. It was found that within the limits of experimental errors, the non-linear oxygen solubility models describe more adequately experimental data for the sensor. Model parameters were defined and analysis of the sensors system performance at different working frequencies and oxygen ranges was made.

Optimum design of pendulum-type tuned mass dampers

The equations of motion are derived for a translational single degree of freedom system equipped with a ‘pendulum-type’ tuned mass damper (TMD) under dynamic force and base acceleration excitations. The complex frequency response functions are obtained. Following response minimization procedures, the optimum parameters of the TMD under random white noise excitations are determined. The effect of the TMD in reducing the response is expressed in terms of an equivalent viscous damping. The optimum design parameters and the corresponding efficiency of the TMD under both wind and earthquake dynamic loads are presented in design charts. The effect of the structure inherent and aerodynamic damping on the optimum parameters is studied and simplified charts to account for such effect are provided. Moreover, a design chart for the over-optimum-damped TMDs is presented. The translational-type TMD is treated as a special case of the pendulum-type. Copyright © 2005 John Wiley & Sons, Ltd.

Evaluation of frequency dependent rubber mount stiffness and damping by impact test

A simple experimental method is presented in this paper to evaluate the frequency dependent rubber mount stiffness and damping characteristics by utilizing the measured complex frequency response function from impact test and by least-squares polynomial curve fitting the data obtained from the test. The study shows the transition of the rubber mount stiffness from static to dynamic values. Using the experimentally estimated values of the rubber mount stiffness and damping, the dynamic response of the tested spring-mass system using a rubber mount as the elastic element can be accurately reproduced. In contrast, it is found that the single degree of freedom ideal spring-mass model using constant stiffness and damping values can only predict the response of the system accurately at resonance but not at non-resonance frequencies. The proposed method is validated by comparing its results with those obtained by using mechanical shaker excitations and those of conventional direct stiffness method using blocked transfer frequency response functions.

Measurement and Modeling of an Ultra-Wide Bandwidth Indoor Channel

This paper describes the results of frequency-domain channel sounding in residential environments. It consists of detailed characterization of complex frequency responses of ultra-wideband (UWB) signals having a nominal center frequency of 5 GHz. A path loss model as well as a second-order autoregressive model is proposed for frequency response generation of the UWB indoor channel. Probability distributions of the model parameters for different locations are presented. Also, time-domain results such as root mean square delay spread and percent of captured power are presented.

Performance of a multi-story structure with a resilient-friction base isolation system

Complex frequency response functions and excitation–response relations for stationary random process are formulated to estimate responses of multi-story superstructures isolated with resilient-friction base isolation (R-FBI) system. The equivalent linearization technique is also used to linearize the nonlinear governing equations of motion of R-FBI system occurred between the parallel actions of the resiliency of rubber and friction of Teflon-coated plates. In this approach, the spectral density functions for both the relative displacement response and absolute acceleration response of N degrees of freedom systems are derived. The applicability and accuracy of the proposed methodology are examined by comparing the resulting responses obtained from this study with those calculated from time history analysis based method. These two studies demonstrate good agreement in terms of characteristics of peak responses. Extensive sensitivity analysis to find the influence of various important structural parameters on the behavior of structures isolated with R-FBI system is also carried out.

유한요소모델에 기초한 3층 건물모델의 시스템 식별

본 연구에서는, 능동질량감쇠기가 설치된 3층 건물 축소 실험을 통해 유한요소모델에 기초한 시스템 식별기법의 유효성을 검증하였다. 입력 신호로는 능동질량감쇠기를 통해 구현되는 20개의 가우시안 백색잡음을 사용하였으며, 출력 신호로는 각층에 설치된 가속도계를 사용하여 측정된 각층 절대가속도를 사용하였다. 복소진동수응답함수를 구성한 후, 마코프(Markov) 파라메터와 시스템 행렬을 추출하였으며, 이로부터 CBSI기법을 이용하여 유한요소모델을 식별하였다. 식별된 유한요소모델과 실험을 통해 얻어진 복소응답함수는 매우 일치함을 확인할 수 있었다. In this paper, an experimental verification of system identification technique for constructing finite element model is conducted for a three-story test structure equipped with an active mass driver (AMD). Twenty Gaussian white noises were used as the input for AMD, and the corresponding accelerations of each floor are measured. Then, the complex frequency response function (FRF) for the input, the force induced by the AMD, was obtained and subsequently, the Markov parameters and system matrices were estimated. The magnitudes as well as phase of experimentally obtained FRFs match well with those of analytically obtained FRFs.

An amplitude equation for the non-linear vibration of viscoelastically damped sandwich beams

An elementary theory for non-linear vibrations of viscoelastic sandwich beams is presented. The harmonic balance method is coupled with a one mode Galerkin analysis. This results in a scalar complex frequency–response relationship. So the non-linear free vibration response is governed by only two complex numbers. This permits one to recover first the concept of linear loss factor, second a parabolic approximation of the backbone curve that accounts for the amplitude dependence of the frequency. A new amplitude–loss factor relationship is also established in this way. The forced vibration analysis leads to resonance curves that are classical within non-linear vibration theory. They are extended here to any viscoelastic constitutive behaviour. This elementary approach could be extended to a large class of structures and in a finite element framework. The amplitude equation is obtained in closed form for a class of sandwich beams. The effects of the boundary conditions and of the temperature on the response are discussed.

How can one tell if noisy frequency response data contain a modal contribution?

A key question that arises in some techniques for experimental modal analysis is whether coherent modal information is buried within a frequency band of complex frequency response data. This question is especially problematic if the data are contaminated by a substantial level of noise. Furthermore, some identification algorithms introduce small anomalies to the data in the course of processing. To explore techniques for resolving this issue frequency response data for a one-degree-of-freedom system is generated analytically and contaminated with various levels of white noise. Five statistical measures are computed for a sequence of bands that are obtained by forming overlapping halves of the previous frequency bands. The five measures are the expected value, mean-square, and variance of the frequency response in each band, as well as eigen-analysis of the autocorrelation matrix and wavelet decomposition. Graphical results are presented and discussed, and an analytical assessment method is proposed.