Advanced frequency domain

In Chap. 18 we will define mathematically the sampling process, derive the z transforms of common functions (learn our German vocabulary) and develop transfer functions in the z domain. These fundamentals are then applied to basic controller design in Chap. 19 and to advanced controllers in Chap. 20. We will find that practically all the stability-analysis and controller-design techniques that we used in the Laplace and frequency domains can be directly applied in the z domain for sampled-data systems. 

Recent advances in ultrashort laser technology has enabled us to investigate dynamics of molecules in a time domain, and furthermore, the success of a theoretical interpretation of the results of time-domain experiments by a moving wavepacket on a potential energy surface (PES) impressively demonstrated the importance of time-domain experiments [1]. On the other hand, it is well-known that a spectrum in a frequency domain and an autocorrelation function in the time domain can be transferred with each other via a Fourier transformation [2]. Therefore, it can be said that the spectrum... 

The best approach, adapted from an earlier proposal by Tomlinson and Hill (19), is to specify the desired frequency-domain excitation profile in advance, and then syntheize its corresponding time-domain representation directly via inverse Fourier transformation. The result of the Tomlinson and Hill procedure is shown at the bottom of Figure 2, in which a perfectly flat, perfectly selective frequency-domain excitation is produced by the time-domain waveform obtained via inverse Fourier transformation of the desired spectrum. 

In general, the quantities being determined by microwave measurements are complex reflection and transmission coefficients or complex impedances normalized to the impedances of the transmission lines connecting a network analyser and the device-under-test (dut). In addition to linear frequency domain measurements by means of a network analyser the determination of possible non-linear device (and thus material) properties requires more advanced measure-... 

The next big advance towards higher precision was the 1997 phase-coherent measurement of the frequency gap with an optical frequency interval divider chain [27]. The 2.1 THz gap was no longer measured by counting cavity fringes, but divided down to the radio frequency domain by a phase-locked chain of five optical frequency interval dividers [56] (see Fig. 5). The accuracy of this approach was limited by the secondary frequency standard to 3.4 parts in 1013, exceeding the accuracy of the best previous measurements by almost two orders of magnitude. 

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... 

The unification of the frequency domain up to 10 Hz has been primarily the result of advances in e qjerimental technique, notably the development of laser sources and of interferometric spectroscopy in the far-i.r. As a result it has become necessary, for the theoretical interpretation of the measurements, to take account in detail of the ways in which the random motions of molecules diiSer from simple difiiision of position or of orientation. ... 

Being able to zoom in is a nice feature, but what if one does not know what to zoom in on, which is the most likely situation in chemical applications. We do not usually know what tiling of the time-frequency domain is most suited for, let us say, our NIR spectrum. Fortunately, one does not need to know this in advance. Techniques exist that select the best basis for a particular situation from the wealth of bases offered by wavelets and wavelet packets. 

Recently Liebert et al. have demonstrated that advanced TCSPC is able to record effects of brain activity with 50 ms time resolution, clear separation of scattering and absorption, and probably better depth resolution than CW or frequency-domain techniques [324, 327, 328]. A system of four parallel TCSPC modules with four individual detectors and several multiplexed laser diode lasers is used. A fast sequence of time-of-flight distributions is recorded in consecutive time intervals of 50 to 100 ms. Variations of the optical properties in the brain are derived from the intensity and the first and second moments of the time-of-flight distributions [325]. 

Measurement of the donor lifetime, which typically is 2-25 nsec, requires adequate time resolution. Two techniques, time-correlated singlephoton counting and frequency-domain fluorimetry modulation, can be used (see A. R. Holzwarth, this volume [14]). Excellent books have been written which include discussion of each technique, and Lakowicz and co-workers have discussed advances infrequency-domain instrumentation and applications to FRET. Donor lifetime measurements, unlike steady-state measurements, are capable of detecting multiple donor-acceptor transfer efficiencies in the sample. These lead to multiexponential decays. Donor lifetime measurements are also not affected by an inner-filter effect... 

The initi findings of the Tg depression in PLLA were ex situ characterization by thermal analysis. In the remainder of this section the use of advanced characterization methods is illustrated to provide additional insight into the novel behavior. The methods used to address the polymer were those appropriate to provide in situ, real-time information on morphology via SALS, and on segmental dynamics via DRS. The rationale for the use of these tools is that the dipolar loss peak in the frequency domain (from DRS) is closely related to the glass transition of a given polymer system — hence, under isothermal conditions, a change in the loss peak frequency is... 

CrCAHERTZ FREQUENCY-DOMAIN FLUOROMETRY Advanced Topic ... 

---