Time-domain techniques

The photon-economy depends on extrinsic sources of noise, the characteristics and settings of the instrument and also on the analysis method. Usually, the photon-economy depends on the lifetime therefore it is instructive to construct graphs of F as a function of the lifetime. The photon-economy of time-domain techniques has been extensively characterized [10, 14, 32, 33],... 

Electron spin echoes (ESE) were first observed in 1958 by Blume1071. In the last few years this time domain technique has found several interesting applications. For comprehensive summaries on the subject, the reader is referred to the review articles of Mims108) and Norris et al.109) and to the monograph of Kevan and Schwartz1101. 

Frequency domain techniques offer advantages over time domain techniques for real-time applications. In the frequency domain the measurements are performed within limited frequency bandwidths. The noise in limited bandwidths is reduced, in most cases substantially. Figures 9.7 illustrates this concept. In Figure 9.7a the... 

This comparison between time and frequency domain measurements is performed at submegahertz frequencies in order to avoid the issue of deconvolution of time domain signals. At megahertz frequencies time domain measurements encounter an additional limitation, these signals must be deconvoluted to isolate the sensor response from the instrument response. The need for deconvolutions adds extra software and computation time, which limits the versatility of time domain techniques for real-time applications. No deconvolutions are necessary in the frequency domain as shown below. 

Other pathways of 3PWr, formation have also been discussed.224 The RP mechanism leads to EPR spin polarization.22 3P7oo has first been observed by Frank et al,225. 3P7oo is short-lived (< 1 ms) and is thus studied by time-domain techniques like transient and pulse EPR.14 If only the iron-sulfur centres are pre-reduced, the radical pair P700, Aj is formed (see below). 

This chapter is organized as follows By reference to a signal model, time-scale and pitch-scale modifications are defined in the first part. The second part presents frequency-domain techniques while the third part describes time-domain techniques. In the fourth part, the limitations of time-domain and frequency-domain methods are discussed along with improvements proposed in the last few years. 

Historically, the first techniques designed to achieve independet control over pitch or duration were carried out in the time domain Fairbanks, Everitt and Jaeger s modified tape recorder [Fairbanks et al., 1954] probably is the first known automatic time-domain system for speech transposition. By contrast with frequency-domain methods, time-domain techniques for time or pitch scale modification manipulate short-duration time-segments extracted from the original signal, a mechanism usually called sampling or splicing As a result, they tend to require much fewer calculations and lend themselves quite well to real-time implementations. 

Here Ti is the energy (or population) lifetime that can be directly measured with other time-domain techniques (4,21). The constants T2 a-T2 c represent pure dephasing contributions not changing the vibrational population (52,53). The following interactions have to be considered (20,53) ... 

Harvey and Hoekstra (1972) determined the dielectric constant and loss for lysozyme powders as a function of hydration level in the frequency range 10 —10 Hz. At water contents less than 0.3 h, they found a dispersion at 170 MHz, which increased somewhat with increasing hydration, and a new dispersion at about 10 Hz that develops at high hydration. These dispersions, detected by time-domain techniques, remain measurable down to the lowest temperature studied, — 60°C. Water mobility in the hydration shell below 0 C is in line with other observations of nonfreezing water. Above 0.3 h, in the stage of the hydration process at which condensation completes the surface monolayer, water motion increased strongly with increased hydration (Fig. 11). 

It is likely that the next few years will see the extension of experiments in this field in two ways (i) the exploitation of time-domain techniques will undoubtedly produce data of wider scope than exist at present OOthe submillimetre band of frequencies (300—5000 GHz), in which some measurements have already been made, will be exploited in numerous, and hopefully systematic, measurements. Probably the theories that are discussed in this article cannot be fully tested until these new extensions of the experimental data come about. The intention of the present discussion is to review the ideas that have already arisen, in order that the need for the extension of data may be properly assessed. 

Much of the high-frequency work that has been done on aqueous non-electrolyte solutions has yielded data at too few frequencies for an analysis of them to be free from ambiguity. It is to be hoped that the new time-domain techniques will remedy this deficiency. 

Measurements on monosaccharides, by Tait et oA, using time-domain techniques, have extended over the wide frequency range 10 - 10 Hz. Using both the original direct time conversion of the data and the full Fourier transform analysis, three separate relaxation times were found. Their values at 278 K and the activation energies are as follows ... 

In spite of its prevalence in the fluorescence decay literature, we were not universally successful with this fitting method. Most reports of hi- or multiexponential decay analysis that use a time-domain technique (as opposed to a frequency-domain technique) use time-correlated photon counting, not the impulse-response method described in Section 2.1. In time-correlated photon-counting, noise in the data is assumed to have a normal distribution. Noise in data collected with our instrument is probably dominated by the pulse-to-pulse variation of the laser used for excitation this variation can be as large as 10-20%. Perhaps the distribution or the level of noise or the combination of the two accounts for our inconsistent results with Marquardt fitting. 

N. V. Kantartzis and T. D. Tsiboukis, Wideband numerical modeling and performance optimisation of arbitrarily-shaped anechoic chambers via an unconditionally stable time-domain technique, ElectricalEngr., vol. 88, pp. 55-81, Nov. 2005.doi 10.1007/s00202-004-0252-4... 

N. Bushyager, J. Papapolymerou, and M. M. Tentzeris, A composite cell-multiresolution time-domain technique for the design of antenna systems including electromagnetic band gap and via-array structures, IEEE Trans. Antennas Propag, vol. 53, no. 8, pp. 2700-2710, Aug. 2005.doi 10.1109/TAP.2005.851832... 

Time-domain technique for the solution of the model distortion equations... 

Model acceptance criteria for the time-domain technique explainability... 

Unlike the transfer-function-based technique, the time-domain technique does not require the central values of the nominally constant parameters to be determined from a minimization exercise. Nevertheless, we will expect the modeller to use sensible estimates, which may be expressed as a condition similar to inequality (24.52) ... 

The most commonly used experimental techniques probe molecules in the frequency domain rather than in the time domain. As emphasized recently (1) the increased level of detail provided by frequency-domain methods produces a more complete picture of the vibrational energy redistribution process, invalidating frequently made claims that time domain techniques, being more direct, are somehow superior. The molecular eigenstate spectra provided by high-resolution experiments currently provide the most complete picture of molecular dynamics. Of course, the frequency-domain and time-domain viewpoints are complementary and we frequently obtain enhanced understanding by considering both viewpoints. 

---