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Excitation and response

The selectivity of the excitation is characterized by the bandwidth of the magnetization response. The response spectrum is determined by the Fourier transform of the selective pulse only in first order. Generally, the NMR response is nonlinear, and nonlinear system theory can be applied for its analysis (cf. Section 4.2.2). A model suitable for describing the NMR response in many situations applicable to NMR imaging is given by the Bloch equations (cf. Section 2.2.1). They are often relied upon when designing and analysing selective excitation (Frel). [Pg.151]

An instructive approach to the linear and nonlinear response is the perturbative analysis of the Bloch equations in the frequency domain [Houl]. The linear response of the transverse magnetization [Pg.151]

Following the nomenclature used in system theory (cf. Section 4.2), the excitation is denoted by x(t). To avoid confusion with the space coordinate x, the time dependence is always explicitly carried along. In general, the excitation is applied in quadrature, that is, in both transverse directions of the rotating frame. [Pg.151]

In the linear approximation valid for small flip angles, the longitudinal magnetization is unaffected by the rf excitation, and the transverse magnetization is proportional to the [Pg.151]

Using this approximation for arbitrarily time-dependent excitation x(t) one obtains a first-order differential equation for the transverse magnetization. [Pg.152]


Although ACh does not have a primary excitatory role like glutamate in the CNS, it does increase neuronal excitability and responsiveness, through activation of muscarinic receptors. It achieves this in two ways, both of which involve closure of K+ charmels (see Chapter 2 and Brown 1983 Brown et al. 1996). The first is a voltage-dependent K+ conductance called the M conductance, Gm or Im. It is activated by any... [Pg.126]

In the following, we will focus our discussion on reactions occurring in clusters in which one chromophore is surrounded by the solvent molecules the reactions occur when the chromophore is excited in its first excited state or ionized. The interest of using a, chromophore within the cluster is that multiphoton ionization can be used in connection with mass spectrometry. In this case, the ionization is a soft process and the spectroscopy of the cluster can give information on the size of the cluster, which is excited and responsible for the reactive event. This assigment can be difficult in other methods (electron bombardment) due to fragmentation processes associated with ionization. [Pg.117]

The dielectric is often assumed to be isotropic in order to simplify Eq. (8) by assuming transverse phonon-polaritons the extension to anisotropic media is straightforward (31). In the limit of very short pulse duration compared to the phonon-polariton oscillation period, the time-dependence of the excitation field can be treated as a delta function, and the phonon-polariton response is given by the impulse response function for the spatial excitation pattern used. If crossed excitation pulses are used, then it is simplest to describe the excitation and response in terms of the excitation wavevector or wavevector range. [Pg.546]

Figure 5.6 Excitations and responses in linear shear relaxation experiments. Figure 5.6 Excitations and responses in linear shear relaxation experiments.
The terms transformation, convolution, and correlation are used over and over again in NMR spectroscopy and imaging in different contexts and sometimes with different meanings. The transformation best known in NMR is the Fourier transformation in one and in more dimensions [Bral]. It is used to generate one- and multi-dimensional spectra from experimental data as well as ID, 2D, and 3D images. Furthermore, different types of multi-dimensional spectra are explicitly called correlation spectra [Eml]. It is shown below how these are related to nonlinear correlation functions of excitation and response. [Pg.125]

Impulse-response and transfer functions can be measured not only by pulse excitation, but also by excitation with monochromatic, continuous waves (CW), and with continuous noise or stochastic excitation. In general, the transformation executed by the system can be described by an expansion of the acquiired response signal in a series of convolutions of the impulse-response functions with different powers of the excitation [Marl, Schl]. Given the excitation and response functions, the impulse-response functions can be retrieved by deconvolution of the signals. For white noise excitation, deconvolution is equivalent to cross-correlation [Leel]. [Pg.125]

Fig. 4.1.1 Interrelationship between excitation (left) and response (right) in spectroscopy (a) Excitation with continuous waves (CW excitation) directly produces the spectrum, (b) For pulsed excitation, the spectrum is obtained by Fourier transformation of the impulse response, (c) For stochastic excitation, the impulse response is derived by cross-correlation of excitation and response signals. Fig. 4.1.1 Interrelationship between excitation (left) and response (right) in spectroscopy (a) Excitation with continuous waves (CW excitation) directly produces the spectrum, (b) For pulsed excitation, the spectrum is obtained by Fourier transformation of the impulse response, (c) For stochastic excitation, the impulse response is derived by cross-correlation of excitation and response signals.
Fig. 4.3.1 [Bliil] The cross-correlation function C (ct) of linear response yx (t) and stochastic excitation x t) is proportional to the impulse-response function, and depends on the time delay a between excitation and response. Fig. 4.3.1 [Bliil] The cross-correlation function C (ct) of linear response yx (t) and stochastic excitation x t) is proportional to the impulse-response function, and depends on the time delay a between excitation and response.
Therefore, for measurements with noise excitation, the linear transfer function K (co) (cf. Fig. 4,1.1 (a)) is obtained after cross-correlation of excitation and response and subsequent Fourier transformation of the cross-correlation function Ci (tr) (cf. Fig. 4.1.1 (c)). [Pg.134]

Cellular Calcium Regulation Calciiun plays critical roles in cellular communication and regulation. The normally very low resting free ionized concentration of Ca is maintained by a variety of ion channels, pumps, and intracellular storage processes. The elevation of intracellular Ca levels during cell stimulation serves to couple information with cellular response -stimulus-response coupling. The control of Ca " homeostasis represents, therefore, a potentially powerful control of cellular excitability and response [ 5 ]. [Pg.220]

Notable recent developments in the realm of low-temperature large, finite, quantum systems pertain to the exploration of homonuclear molecular clusters (aggregates or nanodroplets) of ( He)jy where the nuclear dynamics, elementary excitations, and response are dominated by quantum effects and by permuta-tional symmetry [50-68, 155]. Some of the features of the finite " He boson systems [50, 65, 66, 155-162, 192] are ... [Pg.272]

The d3niamic instrument uses the method of sinusoidal excitation and response. In this case, the applied force and the resulting deformation both vary sinusoidally with time, the rate usually being specified by the frequency f in cycles/sec or w = 2 tt f in radians/sec. For linear viscoelastic behavior, the strain will alternate sinusoidally but will be out of phase with the stress. [Pg.82]

We will now give a very general description of the black box and how to characterize it electrically, irrespective of the box content. The black box may be considered to contain the real tissue with electrodes for excitation and response measurement, or our model in the form of an electric network as a combination of lumped (discrete) electrical components. The network may be with two, three, or four external terminals (compare the number of electrodes used). A pair of terminals for excitation or recording is called a port. The treatment is so general that the content can be characterized with global variables not particularly linked with electrophysiology. [Pg.255]

Driving point immittance is defined with excitation and response at the same port, the result is not influenced hy any contrihution from transmittance components. There are two possible ratios vi/ii (impedance) and ii/vi (admittance). [Pg.256]

Transmittance is defined with excitation and response at different ports. The transfer function H(w) of voltages at two different ports is ... [Pg.256]

In black box theory the excitation (input) and output ports must be defined, the transmission direction must be defined. A network is reciprocal if the ratio between excitation and response remains unaltered when the ports of excitation and response are interchanged. Then the transfer immittances are equal, Y12 = Y21 and Z12 = Z21. Tissue is reciprocal only if it is... [Pg.258]

Up to this point we have described methods in which impedance is measured in terms of a transfer function of the form given by Eq. (56). For frequency domain methods, the transfer function is determined as the ratio of frequency domain voltage and current, and for time domain methods as the ratio of the Fourier or Laplace transforms of the time-dependent variables. We will now describe methods by which the transfer function can be determined from the power spectra of the excitation and response. [Pg.165]

The purpose of this paper is to present the density matrix formalism of angular momentum with half- and integer spin quantum numbers using the spectrum dissolving theorem. The density matrix formalism was developed for the laboratory and rotating frame in order to obtain a complete analytical representation for the spin excitation and response scheme. The density matrix contained in the rotation operator will beeome elear, as oppossed to the approximate treatment, and thereby from the theoretieal process of off-resonance to that of just-resonance through the state of near-resonance will be visualized continuously. [Pg.180]

Figure 9. DBA excitation and response. The mobility of ions and dipoles is measured applying a sinusoidal voltage to the sample and measuring the current. (Reprinted with permission.) ... Figure 9. DBA excitation and response. The mobility of ions and dipoles is measured applying a sinusoidal voltage to the sample and measuring the current. (Reprinted with permission.) ...
In analysis, the response of a system is sought if the system model and excitatimi are known. This is sometimes termed a forward problem. In this interpretation, the inverse problem of finding a system model given the excitation and response is called system identification. System identification in the time domain involves the determination of unspecified parameters of an assumed system model. This can always be formulated as an optimization problem. In the present context, suppose the differential model of hysteresis is adopted and a set of measured excitation-response data from cyclic performance tests of an inelastic structure is given. How can the loop parameters of hysteresis be estimated from the measured data For each choice of the parameters, the response of the degrading structure subjected to the given excitation can be obtained by numerical simulation. The calculated response data can then be compared to the measured data to see if there are large errors. Obviously, the assumed loop parameters... [Pg.2992]

Generation of Variable Seismic Excitation and Response Spectra... [Pg.3360]

Fig. 1.16. (a) Excitation set-up. (b) Orientation of excitation and response directions determination of operative receptance. [Pg.23]

In general (see Eq. (7.116)) Z is the transfer function between the Laplace transforms of excitation and response In the case of functions of type e the transfer function is also directly the quotient of the forced part of the output signal and the input signal [620], as we can readily convince ourselves using a capacitance as an example. In general this follows from the Laplace transform for cos(wt + p). For cos(wt + <,3) / coswt [623] we get cos — = sini this yields... [Pg.465]


See other pages where Excitation and response is mentioned: [Pg.393]    [Pg.180]    [Pg.689]    [Pg.280]    [Pg.281]    [Pg.15]    [Pg.264]    [Pg.343]    [Pg.53]    [Pg.28]    [Pg.137]    [Pg.151]    [Pg.158]    [Pg.242]    [Pg.159]    [Pg.21]    [Pg.264]    [Pg.199]    [Pg.39]    [Pg.174]    [Pg.497]    [Pg.113]    [Pg.493]   
See also in sourсe #XX -- [ Pg.151 ]




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