Time-domain methods

The complete Fourier transformation of current-transient data involves very extensive numerical computation, and two approximate methods have often been used instead. The first method, known as the Hamon (1952) approximation, is based on the assumption that the current transient conforms to the equation 

From the definitions given in Section 4.4.2, it is apparent that the interfacial impedance can be calculated from the perturbation and response in the time domain, in which the excitation can be any arbitrary function of time. In principle, any one of several linear integral transforms can be used (Macdonald and McKubre [1981]) to convert from the time domain into the frequency domain, but the two most commonly used are the Laplace and Fourier transforms  

A number of quantization techniques are available, and the selection of the optimum analog-to-digital converter (ADC) for a particnlar application is properly based on considerations of resolution (precision), accnracy (initial and drift with time and temperature), ease of interfacing, cost, and convenience (availability, size and power requirements). To select an ADC, it is usefnl to nnderstand exactly what types are available and how they work. The fisting in Table 3.1.1, althongh far from complete, does include the most popular ADCs, especially those currently prodnced in an integrated circuit form. 

We will discuss here only successive-approximation and integration ADCs in any detail. The tracking A/D and voltage-to-frequency converter can be looked on as variations of the successive-approximation and the integration design techniques in these types, the digital data is available on a virtnally continuous basis. 

Successive High speed Precision expensive Multiplexing 

Integrating High accuracy Low cost Low sensitivity to noise Low speed DC-100 Hz Digital voltmeters 

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The state-space approach is a generalized time-domain method for modelling, analysing and designing a wide range of control systems and is particularly well suited to digital computational techniques. The approach can deal with... 

Futamata, M., Maruyama, Y. and Ishikawa, M. (2003) Local electric field and scattering cross section of Ag nanopartides under surface plasmon resonance by finite difference time domain method. J. Phys. Chem. B, 107, 7607-7617. 

A number of solid compounds have been examined with this time-domain method since the first report of coherent phonons in GaAs [10]. Coherent phonons were created at the metal/semiconductor interface of a GaP photodiode [29] and stacked GaInP/GaAs/GalnP layers [30]. Cesium-deposited [31-33] and potassium-deposited [34] Pt surfaces were extensively studied. Manipulation of vibrational coherence was further demonstrated on Cs/Pt using pump pulse trains [35-37]. Magnetic properties were studied on Gd films [38, 39]. 

In the time-domain detection of the vibrational coherence, the high-wavenumber limit of the spectral range is determined by the time width of the pump and probe pulses. Actually, the highest-wavenumber band identified in the time-domain fourth-order coherent Raman spectrum is the phonon band of Ti02 at 826 cm. Direct observation of a frequency-domain spectrum is free from the high-wavenum-ber limit. On the other hand, the narrow-bandwidth, picosecond light pulse will be less intense than the femtosecond pulse that is used in the time-domain method and may cause a problem in detecting weak fourth-order responses. 

Our analysis is based on solution of the quantum Liouville equation in occupation space. We use a combination of time-dependent and time-independent analytical approaches to gain qualitative insight into the effect of a dissipative environment on the information content of 8(E), complemented by numerical solution to go beyond the range of validity of the analytical theory. Most of the results of Section VC1 are based on a perturbative analytical approach formulated in the energy domain. Section VC2 utilizes a combination of analytical perturbative and numerical nonperturbative time-domain methods, based on propagation of the system density matrix. Details of our formalism are provided in Refs. 47 and 48 and are not reproduced here. 

As shown in Section 11.2.1.1, more details can be obtained by confocal fluorescence microscopy than by conventional fluorescence microscopy. In principle, the extension of conventional FLIM to confocal FLIM using either time- or frequency-domain methods is possible. However, the time-domain method based on singlephoton timing requires expensive lasers with high repetition rates to acquire an image in a reasonable time, because each pixel requires many photon events to generate a decay curve. In contrast, the frequency-domain method using an inexpensive CW laser coupled with an acoustooptic modulator is well suited to confocal FLIM. 

There are a variety of feedback controller tuning methods. Probably 80 percent of all loops are tuned experimentally by an instrument mechanic, and 75 percent of the time the mechanic can guess approximately what the settings will be by drawing on experience with similar loops. We will discuss a few of the time-domain methods below. In subsequent chapters we will present other techniques for tinding controller constants in the Laplace and frequency domains. 

Finally, a brief discussion is given of a new type of control algorithm called dynamic matrix control. This is a time-domain method that uses a model of the process to calculate future changes in the manipulated variable such that an objective function is minimized. It is basically a least-squares solution. 

Chu, S.T. and Chaudhuri, S.K., 1989, A finite-difference time domain method for the design and analysis of guided-wave optical structures, J. Lightwave Technol. 7 2033-2038. 

All methods mentioned in Table 1 operate (typically) in the frequency domain a monochromatic optical wave is usually considered. Two basically different groups of modeling methods are currently used methods operating in the time domain, and those operating in the spectral domain. The transition between these two domains is generally mediated by the Fourier transform. The time-domain methods became very popular within last years because of their inherent simplicity and generality and due to vast increase in both the processor speed and the memory size of modem computers. The same computer code can be often used to solve many problems with rather... 

A. Taflove and S.C. Hagness, Computational electrodynamics the finite-difference time-domain method, 2 ed., (ArtechHouse, Norwood, 2000). 

Many interesting phenomena can arise in nonlinear periodic structures that possess the Kerr nonlinearity. For analytic description of such effects, the slowly varying amplitude (or envelope) approximation is usually applied. Alternatively, in order to avoid any approximation, we can use various numerical methods that solve Maxwell s equations or the wave equation directly. Examples of these rigorous methods that were applied to the modelling of nonlinear periodical structures are the finite-difference time-domain method, transmission-line modelling and the finite-element frequency-domain method." ... 

K. L. Shlager, and J. B. Schneider, A survey of the finite-difference time domain literature, in A. Taflove (Ed,), Advances in computational electrodynamics the finite difference time domain method (Artech House, 1998), pp. 1- 62. 

Kunz, K. S., and Luebbers, R. J. 1999. The finite difference time domain method for electromagnetics. Boca Raton CRC Press. 

A considerable amount of mechanistic information is accessible through a direct, time-domain, method first proposed by Steele as a general approach to analyzing and approximating collective TCFs. The approach has been apphed to SD jQ other observable relaxation processes in liquids. It is... 

In this chapter I have presented the basics of SD and described several approaches that can be used to uncover the molecular mechanisms contributing to SD both within the LRA and when the response is nonlinear. Within the LRA, I discussed INM and time-domain methods for analyzing the solvation TCP and the related solvation velocity time correlation, G(f). The methods were illustrated by showing how they can determine the relative contributions to SD from different molecules, types of molecular motion, and correlations among solvent molecules. I also discussed how they can be used relate SD to other observable dynamics in liquids and to explore the similarities and differences between SD in... 

This is the phenomenon of the so-called constant phase element (CPE) as it follows from eqn. (115) that Yc is composed of an imaginary and a real component, with a frequency-independent phase angle cor/2. Though the phenomenon is most clearly discovered in impedance or admittance analyses, its effect in time-domain methods should not be ignored. 

Most time-domain methods are based on this simple idea, and differ only in the choice of the segment durations, splicing times and weighting windows. They can be classified according to whether they make use of pitch information or not. 

Conclusion. The development of low-complexity time-domain methods for time-scale or pitch-scale modifications has already made it possible to incorporate such systems in consumer products such as telephone answering systems, effect boxes and semi-professional CD players. They could easily be implemented in record or playback devices such as DAT or CD players, offering the user additional control over... 

FDTD finite difference time domain (method)... 

It is appropriate finally to say something about usefulness of time domain methods for study of relaxation processes at megahertz to gigahertz frequencies. The need for improved precision and more complete frequency coverage in this range has been pointed out by several authors, as has the potential usefulness... 

C. Time Domain Methods for Determining the Polarization Resistance... 

The complications and sources of error associated with the polarization resistance method are more readily explained and understood after introducing electrical equivalent circuit parameters to represent and simulate the corroding electrochemical interface (1,16-20). The impedance method is a straightforward approach for analyzing such a circuit. The electrochemical impedance method is conducted in the frequency domain. However, insight is provided into complications with time domain methods given the duality of frequency and time domain phenomena. The simplest form of such a model is shown in Fig. 3a. The three parameters (Rp, Rs, and C d,) that approximate a corroding electrochemical inter-... 

As both the frequency domain and the time domain methods have disadvantages, Boukamp [87] recommended that both methods be combined using the CNLS-fit procedure, data validation (Kramers-Kronig transformation), and deconvolution. The Kramers-Kronig transformation can be found in Appendix C. 

Alternatively, band peak shifts can be computed from at) initio absorption spectra for SO2 isotopologues [28], which is the method I ve used here. The ah initio spectra were computed by time domain methods (Lanczos recursion and Cheby-shev propagation) using a new potential energy surface for SO2. The ah initio... 

Especially at the short times, the use of time domain methods, as opposed to their polnt-by-polnt frequency domain equivalents, is advantageous in a number of ways. They can, for example, be considered as truly spectroscopic techniques because of their broad-band nature and their capacity to generate dielectric properties as a continuous function of time or, Ity appropriate transformation, frequency. In the past few years, time domain methods have received fresh Impetus from advances in two different types of method firstly, the d.c. step response technique as used by Reddish and Williams has been up-graded in sensitivity and bandwidth through... 

Direct numerical Fourier transformation when a wide range of frequencies is involved requires the storage of a very large number of data samples [i (0] d extendve computation. The usual practice in slow-response time-domain methods has consequently been to employ more approximate transformation methods, such as the Hamon approximation. This relates the current per unit voltage at time t, i(/), to the dielectric loss e at the frequency v = 1/10/ by... 

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