Time-domain Impulse Research Articles

A State Space Method for Modal Identification of Mechanical Systems from Time Domain Responses

A new state space method is presented for modal identification of a mechanical system from its time domain impulse or initial condition responses. A key step in this method is the identification of the characteristic polynomial coefficients of an adjoint system. Once these coefficients are determined, a canonical state space realization of the adjoint system and the system′s modal parameters are formulated straightforwardly. This method is conceptually and mathematically simple and is easy to be implemented. Detailed mathematical treatments are demonstrated and numerical examples are provided to illustrate the use and effectiveness of the method.

Compact antenna test range without reflector edge treatment and RF anechoic chamber

There are several types of CATRs (compact antenna test ranges) used in antenna-pattern measurements. An offset reflector is generally used to generate the quiet zone of a CATR. Serrated edges, rolled edges, or R-cards are generally chosen along the reflector's edge to reduce the edge-diffraction field inside the quiet zone of the CATR. In order to reduce stray signals from the environment, a high-quality RF anechoic chamber is required for a CATR. In this paper, a new type of CATR, without either a reflector edge treatment or an RF anechoic chamber, is developed. A commercially available DBS (direct-broadcast satellite) reflector antenna, without edge treatment, is used as the reflector antenna of the CATR to generate the quiet zone of the antenna test range. In order to improve the quiet zone's performance, the fields due to feed spillover, edge diffractions, and other stray signals are gated out by the ITDAMS (impulse time-domain antenna measurement system). The RF interference in the environment can also be reduced by time synchronization and pulse integration of the impulse time-domain antenna measurement system. In order to verify the capabilities of the proposed CATR, three kinds of antennas (a low-directivity horn antenna, a high-directivity 60 cm direct-broadcast satellite reflector antenna, and a 25 cm Ka-band Cassegrain LMDS - local microwave distribution system - antenna) were measured by the proposed CATR. The antenna-pattern results agreed quite well with those of a near-field range and a far-field range.

Lossy transmission line simulation based on closed-form triangle impulse responses

Analytical frequency-domain expressions for single and coupled transmission lines with triangular input waveforms are first developed. The inverse Fourier transform is then used to obtain an expression for the time-domain triangle impulse responses for frequency-independent transmission line parameters. The integral associated with the inverse Fourier transform is solved analytically using a differential-equation-based technique. Closed-form expressions for the triangle impulse responses are given in the form of incomplete Lipschitz-Hankel integrals (ILHI) of the first kind. The ILHI can be efficiently calculated using existing algorithms. Combining these closed-form expressions for the triangle impulse responses with a time-domain convolution method using a triangle impulse as a basis function, provides an accurate and efficient simulation method for very lossy transmission lines embedded within linear and nonlinear circuits.

LiNbO3-based integrated optical network analyser for vectorial structure characterisation of fibre Bragg gratings

A LiNbO3-based integrated optical network analyser for polarisation-resolved longitudinal structure characterisation of optical fibre Bragg gratings is reported. The frequency-dependent complete reflectance Jones matrix is measured by interferometry and transformed into the time-domain impulse response. From the impulse response matrix the vectorial grating structure is determined by inverse scattering. Local dichroic reflectivity and birefringence were derived from this data. Knowledge of the vectorial nature of refractive index modulation depth and phase should allow an improvement of the ultraviolet (UV) illumination process and an effective correction of phase mask errors by longitudinally selective UV light post-processing, in order to fabricate chirped and/or apodised gratings which require the highest fabrication accuracy.

Impulse scattering processes of an elastic sphere

The ‘‘movable rigid sphere’’ scattering model of Hickling and Wang [J. Acoust. Soc. Am. 39, 276–279 (1966)] incorporates the translational ‘‘rebound’’ response of the scatterer to the incident field. However, as a physically unrealizable object, the rigid sphere has limited applicability. Recently, it was shown [J. Acoust. Soc. Am. 106, 553–564 (1999)] that both the movable rigid sphere and Anderson’s fluid sphere model [J. Acoust. Soc. Am. 22, 426–431 (1950)] are limiting cases of Faran’s elastic sphere scattering theory [J. Acoust. Soc. Am. 23, 405–418 (1951)]. In this paper, the time domain impulse response is used to demonstrate the three dimensional scattering of an elastic sphere and its special cases. The critical factor is the shear rigidity modulus. For normal elastic values of the modulus, shear waves dominate the scattering response. When the rigidity is high, the shear waves travel more rapidly through the sphere, and its motion becomes increasingly characterized as a rebound translation without change of shape. Wave conversion at the boundary is also inhibited. For low or vanishing rigidity, only compressional waves are supported, and these determine the scattering response. The presentation will be illustrated by movie animations. [Work supported by ONR.]

A frequency domain model for generating B-mode images with array transducers

A frequency domain B-mode imaging model applicable to linear and phased array transducers was developed for simulating ultrasound images of random media. Computations are based on an approximation that is less restrictive than the Fresnel approximation. The model is compared with the exact time domain impulse response method, regarded as the "gold standard". In a typical application, errors in simulated rf waveforms are less than 1% regardless of the steering angle for distances greater than 2 cm, yet computation times are on the order of 1/150 of those using the exact method. This model takes into account the effects of frequency-dependent attenuation, backscattering, and dispersion. Modern beam-forming techniques such as apodization, dynamic aperture, elevational focusing, multiple transmit focusing and dynamic receiving focusing also can be simulated.

Buried thermoplastic layer diagnostics by the use of combined frequency-domain and impulse response photo-thermo-mechanical radiometry

A photothermal approach to the problem of characterizing the thermoplastic layer thickness sandwiched between two metal foils used in heat-sealed food containers is described. Real-time signal acquisition instrumentation for the photothermal radiometric signal based on impulse-response fast Fourier transform (FFT) processing via chirped laser-beam modulation and cross-correlation spectral analysis, instead of the conventional point-by-point discrete frequency scans with a lock-in amplifier has been introduced. A theoretical frequency-domain model for the signal generation due to laser heating, which contains both a thermal component and a mechanical component due to the thermal expansion of the thermoplastic layer, is presented. The time domain impulse response theoretical data have been obtained by a numerical FFT of the frequency-domain theoretical data. The total signal was measured via radiometric detection in both domains and was fitted to the theory to obtain thermal transport properties of the three-layered system. The thickness of the thermoplastic layer has been extracted with better than 5% precision.

Single-cycle waveforms and non-periodic waves in dispersive media (exactly solvable models)

Exactly solvable models for impulse time domain electromagnetics of dispersive media are developed to describe the interaction of ultrashort (single-cycle) transients with certain classes of insulators and conductors. Transient-excited fields are described analytically by means on new, exact, non-periodic and non-stationary solutions to Maxwell's equations, obtained directly in the time domain without using Fourier-expansion or time-space separation methods. Such non-separable solutions form the mathematical basis of non-periodic waves optics. Extensions to spherical and MHD single-cycle transients, shock-excited distributed transmission lines, and some inhomogeneous and nonlinear media are presented. A flexible technique for modeling real transients by Laguerre functions is developed which enables the shape and duration dependence of the refraction and reflection features of single-cycle waveforms to be presented explicitly.

Time Resolved Measurements Which Isolate the Mechanisms Responsible for Terahertz Glory Scattering from Dielectric Spheres

The surface-wave scattering processes responsible, in part, for the optical glory have never been compared with theoretical predictions. Here, THz impulse ranging is used to measure the time domain impulse response of spherical targets with sufficiently high temporal resolution to permit the surfacewave contribution to the total impulse response to be isolated. The first direct experimental comparison for the surface wave with Mie theory as well as the surface-wave approximation of van de Hulst is performed. Interference of the surface waves from a dielectric sphere is shown to lead to the frequency and angular intensity dependence of the THz glory. [S0031-9007(97)04970-3] PACS numbers: 42.25.Fx

Complex-exponential representation of time-domain response of a one-mode resonator

Time-domain response of a one-mode resonator is investigated by using a complex-exponential representation of the time-domain impulse response. The transient response of a resonator has calculated for a short incident pulse which has rectangular form and the radio frequency filling. The convolution integral has been analytically carried out and two solutions for the time histories of the transient response of the resonator have been found. They are the early-time and late-time portions of the signal. The behaviour of amplitude and frequency of the transient response of the electrodynamical structure under consideration is studied.

Calculating the pulsed response of linear arrays: accuracy versus computational efficiency

The accuracy and computational efficiency of different methods for calculating the field profile from linear arrays are examined. Specifically, various approximations used for time and frequency domain solutions are studied and compared to the exact time domain impulse response method, which is taken to be the "gold standard". The accuracy is measured in terms of the error in the 6 dB spatial resolution, whereas the efficiency is represented by the normalized computation time. The results demonstrate that in the frequency domain the Fresnel approximation yields accurate results (errors <1%) for the unsteered array, but that the accuracy degrades with increasing steering angles (>10/spl deg/). It is also shown that, in general, this method is computationally more efficient as compared with the exact method since the efficiency of the latter depends highly on the field point location and array geometry.

Ultrasonic compression wave propagation in adhesive polymers described as a signal filtering process

The ability to test adhesively bonded metal structures non-destructively requires an understanding of ultrasound wave propagation in adhesive materials. This paper presents the results of an experimental study of wave absorption and phase velocity dispersion in a number of structural adhesives in terms of the frequency response and the time domain impulse response of propagation in a thin layer of material. A simple single relaxation time model provides a phenomenological basis on which to consolidate the measured data into a form that can be used to model wave propagation in more complex structures containing an adhesive. It is shown that high rates of attenuation, increasing with frequency, will seriously limit the frequency bandwidth available for ultrasonic non-destructive testing of adhered structures. Extensions to the model are appended that will provide the basis for its implementation by means of linear electric network simulation packages.

Partial discharge signal generation transmission and acquisition

The phase resolved partial discharge detection technique (or 'PD pattern recording technique') is applicable to field measurements, particularly if combined with disturbance rejection techniques and non-conventional pick-up circuits. Electromagnetic disturbances can be eliminated by filtering in the time domain (impulse noise gating) and/or in the frequency domain (down-mixing). The PD patterns not only reveal the PD physics and thus help to identify the defect type, but also serve to evaluate the efficiency of the disturbance rejection procedure.

Photonic wideband array antennas

Presents an introduction to the optical control of array antennas by using fiber optic links for remote control and a photonic time shift network for wide instantaneous bandwidth. An overview of the development of a wideband conformal array designed for airborne surveillance radars is given. The paper covers the system design and the performance of an L-band (850-1400 MHz) M-element array controlled by photonics. Packaging techniques of the photonic components and the array aperture are discussed. The wideband performance of the system is highlighted. A nano-second impulse response has been measured to demonstrate a 50% instantaneous bandwidth (550 MHz, 30 cm range resolution) for target ID and imaging. A built-in signal injection technique based on time-domain impulse measurement was used to calibrate the wideband components in the time-shift beamforming network.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Precise navigation using adaptive FIR filtering and time domain spectral estimation

This paper introduces a new low cost, short range, positioning system based on adaptive finite impulse response (FIR) filtering and time domain spectral estimation. The system can determine absolute positions with a high degree of accuracy and is well suited for real time navigation. The approach is based upon signal processing techniques and a priori knowledge of the system transfer function. The first step is to measure the phase response of the linear transfer function and then using a FIR filter the time response of the system can be determined. The FIR filter computes the time response by performing a deconvolution between the measured phase response, and the complex conjugate of the transfer function. By correlating the known input impulse response with the output of the FIR filter, an error term is generated. The time delay of the system is determined by adjusting the FIR filter coefficients to minimize the error term. Simulated analysis of the system indicates a worst case error of /spl plusmn/16 cm. >

A new algorithm to calculate the transient near-field of ultrasonic phased arrays

An algorithm valid for an accurate calculation of the near-field in the scanning plane of ultrasonic phased arrays is presented. Using the classical time-domain impulse response approach, a simple analytical expression for the impulse response at points lying in the central plane of a narrow rectangular aperture is decided. An expression for the array impulse response is then obtained by superposition. The proposed solution is useful for an efficient computation of transient and continuous wave (CW) pressure fields without requiring any far-field or paraxial approximations. Moreover, the convolution-impulse response approach applied to phased arrays constitutes an important tool for the analysis of array fields. Some numerical examples are presented, in which the advantages of using the array impulse response in the field analysis are shown. Several aspects of array fields not currently described in literature are included in the examples.

The Character of a Scattered Wavelet: Aspherical Obstacle Embedded in an Elastic Medium

Abstract Wavelets scattered from a spherical heterogeneity were computed from solutions of the wave equation for a plane wave incident on a spherical inhomogeneity. The solution is expressed as an orthogonal function expansion that is asymptotically correct for all wavelengths. In this paper we computed the spectral response and corresponding time-domain impulse response for wavelengths greater than one tenth the radius. The frequency content and amplitude of the scattered wave from an incident compressional wave systematically varies with scattering angle. A comparison of the scattered waves with arrival times and amplitudes computed using ray theory shows that the variations in response with scattering angle are closely tied to arrival times and amplitudes of the internally reflected and refracted waves. Use of the minimum phase criterion in order to generate a wavelet does not replicate the wavelet shape, but can be used to generate wavelets where the spectral amplitudes are the principal objective. The Born approximation, the first two terms in the orthogonal function expansion, underestimates the high-frequency energy.

Diffraction impulse response of rectangular transducers

A closed-form expression for the impulse velocity potential of rectangular pistonlike transducers, without any far field or paraxial approximation, is presented. The classical time-domain impulse response approach is used considering free-field, rigid baffle, and pressure release boundary conditions. Previous approaches to the rigid baffled rectangular piston require the use of superposition methods in order to find a general solution numerically. These must add or subtract, according to the field point location, the analytical expressions that were derived only for specific field points or geometrical regions. In this paper the complexity introduced by the geometrical discontinuities of rectangular apertures is analyzed. A new compacting methodology is proposed and applied to obtain a general solution for the impulse response. This new solution provides the value of the impulse response directly in the time domain, without requiring superposition methods. In addition, a closed-form solution for the pressure impulse response is also presented. This can be useful for physical insight and a qualitative analysis of transient and continuous wave pressure fields. Also included is a description of the temporal behavior of the impulse velocity potential and the pressure impulse response for field points in different regions. The proposed solution allows an efficient and accurate computation of pressure fields under realistic excitations. Several examples illustrate the use of this new solution in the computation of transient pressure waveforms, when wideband and relatively narrow-band excitation pulses are used. Three-dimensional plots of the peak amplitude of the transient pressure near field are presented, and certain characteristics are analyzed using the pressure impulse response.

On the presentation of large amounts of architectural acoustics data.

With the proliferation of data acquisition systems that process time domain impulse responses taken in auditoria, there is an overwhelming quantity of (useful) data that can be computed using the digital signal processing algorithms ordinarily supplied with such systems. The example given is a 507-seat lecture hall where two different speech-reinforcement systems were evaluated at 10 spatial locations using MLSSA, generating over 4.8 megabytes of time domain data in less than 2 h. One additional hour of semiautomated postprocessing resulted in 960 important acoustic parameters from a field of 2100 pieces of analytical data, and 1960 modulation transfer function parameters for STI calculations. These multitudinous data are organized into a series of colorful graphs that show a large amount of interconnected information in a single view, and in a way that provides maximum insight to the experienced acoustician, yet can be created easily in a laboratory having a modest software budget and rather ordinary color display and printing means.

A wave vector, time-domain method of forward projecting time-dependent pressure fields

A wave vector, time-domain (k−t) method of forward projecting time-dependent pressure fields from complex vibrators is developed using space-time Fourier transform methods. Axisymmetric fields are included as a special case of the general formulation in which a pressure field at one plane can be forward projected to other planes. In brief, a wave vector, time-domain representation of the field at one plane is forward projected via a temporal convolution with a wave vector, time-domain impulse response that is dependent on the projection distance. The projected field is then obtained via the use of an inverse spatial Fourier transform. A numerical study of the method illustrates the accuracy of the approach when implemented using fast Fourier transform (FFT) algorithms. The forward projections of simulated pressure fields from a planar ultrasonic transducer are shown to be in excellent agreement with corresponding results from the use of a time-domain impulse response method.