Frequency response functions

In such a case, no conclusion about the mechanisms can be reached from the form of 4(t) and the observed rate will be determined primarily by the fastest process. By extension of the argument, one easily sees that marked deviation of any of the parallel processes from exponential decay will be reflected in the overall rate with possible change in the functional form. Thus, if the rotation is described by exp(-2D t) as in Debye-Perrin theory, and the ion displacements by a non-exponential V(t), one finds from eq 5 that 4(t) = exp(-2D t)V(t) and the frequency response function c(iw) = L4(t) = (iai + 2D ) where iKiw) = LV(t). This kind of argument can be developed further, but suffices to show the difficulties in unambiguous interpretation of observed relaxation processes. Unfortunately, our present knowledge of counterion mobilities and our ability to assess cooperative aspects of their motion are both too meagre to permit any very definitive conclusions for DNA and polypeptides. 

Polynomial smoothing does not possess an ideal frequency-response function and can potentially introduce distortions and artifacts in smoothed signals [7], Other methods of smoothing do not possess these shortcomings. A detailed discussion of these important points is presented in Chapter 10. 

We have performed optically heterodyne-detected optical Kerr effect measurement for transparent liquids with ultrashort light pulses. In addition, the depolarized low-frequency light scattering measurement has been performed by means of a double monochromator and a high-resolution Sandercock-type tandem Fabry-Perot interferometer. The frequency response functions obtained from the both data have been directly compared. They agree perfectly for a wide frequency range. This result is the first experimental evidence for the equivalence between the time- and frequency-domain measurements. 

Figure 2 The imaginary part of frequency response function, Im (Au ). obtained by the OHD-OKE (dots) and the light scattering measurements by the double monochromator (dashed line). In the insert is shown Im.R(Au ) obtained by the tandem interferomator (solid line). A small peaic appearing at 3.3 cm (shown as a symbol of ) is the ghost due to the tandem interferometer.

The QS frequency response functions for pressure-perturbed burning (constant radiant flux) and radiation-perturbed burning (constant pressure) have been obtained as... 

Rp = pressure-driven frequency response function = (m/m)/(P /P) at constant qr Rq = radiation-driven frequency response function = (m/m)/(qr /qr) at constant P r=idTsldTo)p ... 

Frequency response Frequency response functions Heat transfer coefficient, W m K ... 

Figure 16.34 Model-based FRF SHM. (a) Composite specimen geometry (b) frequency response function (FRF) up to 2 kHz showing changes due to damage [77].

The target of the work was to improve the level of detail in the analysis of the experimental resjmnse function. Pitting the theoretical (but not the Electrochemical Equivalent Circuits-based) frequency response function to the experimental data is shown to provimetal-insulator interface. On these basis, changes in surface dif-fusivity values might be effectively used to track the evolution of the interface under T H tests, thereby providing a novel tool to predict adhesion failure. 

The dynamic behavior of a system can be characterized using the frequency response function (FRF), which in structural dynamics has the form of a receptance and is defined as... 

Dynamics, Fig. 2 Impact test measurements with different size of modal hammers and a frequency response function... 

Fig, 3 Frequency response function obtained by free boundary component mode synthesis... 

Here, p is the magnitude of pressure fluctuation, c is the speed of sound,/is the frequency of acoustic wave, k = Inf/c is the wave number, z is the axial direction, p is the fluid viscosity, p is the density, R is the radius of tube, v is the kinematic viscosity, and / is the Bessel function. The frequency response function H(f) from Eq. 27 is used to determine the frequency response of the shear stress sensor as... 

The method presented in this chapter is based on nonlinear frequency response and the concept of higher-order frequency response functions, which have been proven as very convenient tools for analyzing weakly nonlinear systems. The basics for their application lay in the facts that ... 

A model of a weakly nonlinear system can be replaced by an indefinite sequence of linear models of different orders. In the frequency domain, these linear models are defined as frequency response functions (FRFs) of different orders, which can be estimated from different harmonics of the FR. 

Frequency response functions. By applying the Fourier transform to the function g(r), the FRF, or frequency transfer function is obtained ... 

Lee, GM., Estimation of nonlinear system parameters using higher-order frequency response functions, Meek Syst. Signal Process., 11, 219-228, 1997. 

However, most sensors used currently in AE applications for concrete are manufactured in a more traditional way, showing either a resonant behavior or several particular resonances. These sensors, which are called multi-resonance transducers, have a higher sensitivity than sensors with a backward mass used outside of their resonance fiequency. Such sensors should not, however, be considered as (true) broadband and it is essential to know their frequency response function. Otherwise, signal characteristics from the source are not distinguishable from artifacts introduced by incorrect knowledge of the frequency response. A calibration of the sensors frequency response, as well as understanding of the direction sensitivity, is important for many applications of AET. 

Fig. 5.5. (top) Example of frequency response functions of a resonant and a so-called broadband transducer. The frequency response function was measured using a laser-vibrometer (middle) and a face-to-face method (bottom). Amplitudes are on a linear scale. 

This definition was introduced by Hall and its application to PZT stacks was also demonstrated by Wang et. al. I Fourier Transformations were used to decompose acquired signals in this study. These decomposed signals served as inputs to determine the frequency response function (FRF) of the stack being tested. The obtained FRF of strain with respect to electric field defines a complex piezoelectric coefficient d as ... 

Jonscher [1974,1975a,b, 1980,1983], in an extensive series of papers, working primarily in the dielectric area, independently emphasized the importance and ubiquity of constant phase response, and proposed and demonstrated the utility of three different empirical frequency response functions in IS data fitting. These three equations, termed universal dielectric response by Jonscher, were originally... 

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