Modulation Schemes

To reduce spurious signals due to drifts of the EPR line setting arising from mechanical and thermal instabilities, double coding of the ENDOR information is often employed Normally a low-frequency Zeeman modulation (30-300 Hz) is applied while the rf field is frequency or amplitude modulated at frequencies of about 1-30 kHz. This modulation scheme, however, has two major disadvantages  

1) For maximum ENDOR enhancement, the Zeeman modulation amplitude has to be about one half of the width of the EPR line which is saturated at an extremum of its first derivative. However, in an EPR spectrum with line widths of typically 1 mT this Zeeman modulation contributes 20 kHz to the width of a proton ENDOR line. It turns out that in many cases a remarkably better resolution of the spectra may be obtained with a single coding in which only the rf field is modulated. 

2) In powder samples with broad EPR lines, large Zeeman modulation amplitudes have to be applied to improve the sensitivity. Such amplitudes often produce microphonic noise in the cavity and cause an uncertainty in the orientation selection in single crystal-like ENDOR spectra (Sect. 4.1). A modulation technique which avoids these problems in powder ENDOR studies has been proposed by Hyde et al.. In this scheme the Zeeman modulation is replaced by a 180° modulation of the phase of the microwave signal. 

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The reflectance, R, is defined as the ratio of the reflected light intensity to the intensity of the incident beam. Usually, one determines the change in reflectance, A/ , induced by some parameter, such as the electrode potential. Experimentally, one measures only the intensity of the reflected beam, 4. So if the incident intensity remains constant, the reflected beam gives hJl/R = A4/4. Experimental results are presented as plots of A/J/R vs. the parameter of interest, such as the frequency of the incident light or electrode potential. Modulation schemes, wherein the beam is chopped or the potential is modulated, are used to enhance the signal-to-noise ratio. 

At the early stages of development, the lack of a convenient and economic excitation modulation scheme has limited the use of such a phase shift technique in fluorescence thermometry. Now with the wide availability of cheap and easily modu-... 

The quality of the profile pertaining to the selected region can be improved by a modulation of the pulse lengths within the pulse train, which mimics the amplitude modulation of a simple soft pulse [8]. Simple modulation schemes can be devised for attenuating or even suppressing the side-lobes in the vicinity of the selected region (as shown in fig. 3). Alternatively, more elaborated modulation schemes as those of the BURP family [9] can be run in the DANTE-Z mode [10]. This mode actually offers a... 

Figure 8. Encoder for the applied coded modulation schemes 4-ary-CC-TCM, 4-ary-ML-1/5-4/5, and 8-ary-SC-TCM.

The goal of any practical modulation scheme is to reduce, or, if possible, eliminate, all the elements of the decoherence matrix in Eq. (4.203) (see Ref. [20] for an alternative solution). However, in order to obtain the optimal modulation [29], one must first know the system-bath coupling spectra of the qubits in question. This information is usually not available a priori and thus most experimentalists have resorted to the suboptimal DD (or bang-bang) modulation, which does not require this knowledge. 

Furthermore, if one has a multipartite system, and thus a decoherence matrix, one must perform multiple modulation schemes that address the different qubits, on top of performing the aforementioned single-qubit scheme for all the qubits. This is essential to ascertain the cross-coupling spectra of all the possible qubit pairs. As discussed in Refs [19, 20, 112], these cross-coupling spectra are extremely important in reducing disentanglement and allow, in certain circumstances, to completely eliminate decoherence. 

After one obtains the system-bath coupling spectra by applying specific, parameterized modulation schemes, one can finally tailor the specific modulation that would optimally reduce or eliminate decoherence. However, two aspects should be... 

The selection of a particular modulation scheme starts by determining which of the sample s Mueller matrix components need to be measured. This decision can be guided by examining the form of the Mueller matrix given in equation (1.18), which contains all... 

Once the matrix elements of interest have been identified, equation (8.2) is used to specify which matrix elements of the PSG and the PSA need to be highlighted. In the subsections to follow, different modulation schemes are presented for the purpose of meeting specific requirements. 

The most important part of any CMB experiment is the modulation scheme that allows one to measure //K signals in the presence of 100 K instrumental foregrounds. A good modulation scheme is much more important than high sensitivity, since detector noise can always be beaten down as l/ /f by integrating longer, while a systematic error is wrong forever. 

Hug first pointed out the virtues of backscattering over ten years ago [89], but unfortunately, he was only able to carry out a few preliminary measurements before his instrument was destroyed by fire. The other area of recent advance, as discussed above, was the introduction of alternative polarization modulation schemes. SCP ROA was measured for the first time with a diode array detector [32], and the first measurements of DCPj ROA coincided with our first measurements of backscattering ROA [35]... 

A complete theory of circular polarization ROA, including all known scattering geometries and polarization modulation schemes, has been presented recently [108], and this theory, combined with linear polarization ROA, has been formulated in a unified way [26,109,110] using the Stokes-Mueller formalism. In addition, progress in the theoretical description and experimental measurement of ROA invariants has been reviewed recently [26]. 

The novel aspect of this experiment was that the confocal cavity was locked to continuous-wave radiation which was frequency shifted by an acousto-optic modulator such as to centre the filtering cavity onto the chirped amplified radiation. This reduced the residual amplifier shift to -2(1 MHz. The dominant contribution to this shift resulted from the cw light being injected off-axis into the cavity. Because the filter cavity had a high finesse we used a phase modulation scheme for locking. Indeed, we normally locked the dye laser to the filtering cavity and scanned the spectrum by scanning the filter cavity. 

The simple spectrometer system illustrated in block diagrammatic form in figure 10.2 would be rather insensitive, but there are many refinements which greatly improve the situation. Perhaps the most important of these is signal modulation and in this section we consider a number of different modulation schemes which have been used to great effect. Modulation has several objectives, but one of them is to convert the output detector signal from d.c. to a.c. a.c. amplification and detection techniques, including phase-sensitive detection, can then be used. 

The PGSE NMR method relies on the use of two sharp gradient pulses separated by a well-defined time interval and is therefore naturally suited to time-domain analysis of motion. However, it is important to realize that this particular form of two-pulse gradient modulation is not unique. In particular, a number of other time-modulation schemes are possible in which the molecular motion is detected in a different manner. However, as we shall see, whenever modulated gradients are used to encode the spin magnetization for motion rather than position, it is appropriate to refocus any phase shift due to absolute spin position by means of a spin echo. Consequently, we refer to this more general type of experiment as modu-... 

As expected the PKS for rapamycin showed a Type I organisation strongly reminiscent of the erythromycin PKS, with catalytic activities arranged in modules (Scheme 27) and with sets of modules housed in turn in three multi-modular cassettes designated RAPS 1, RAPS 2 and RAPS 3. RAPS 1 contains modules 1 to 4, RAPS 2 modules 5 to 10, and RAPS 3 modules 11 to 14. The domain structure of the rapamycin PKS may not correspond in every detail to the pattern expected from the proposed structure for the PKS product however. In modules 3 and 6, there appear to be potentially active KR and DH domains which are not required module 3 also contains a potentially active but functionally redundant ER domain. It is possible that the active sites of these extra domains have been inactivated in a way that is not apparent from the primary sequence, and that the now redundant protein residues have still to be edited out by the random processes of evolution. There is also a chance that all these domains are indeed active and that the true rapamycin PKS product is more fully reduced than that shown. Extra post-PKS reoxidations would then be required to reintroduce the oxygen functionality at the relevant sites in the final structure. 

Binary Modulation Scheme procedure - The procedure receives a sequence h = bi,..., bk) of k bits and a covertext sequence s = si,..., s ) of k transform coefficients. The procedure constructs, for each coefficient Sj, a pair of SBE functions ... 

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