Sine pulse

The amplitude modulated pulses may require special equipment such as a waveform generator which, however, has become a standard constituent of the modem commercial spectrometers. The amplitude modulated pulses are usually windowless and the sidebands produced by these pulses, in most cases, are very weak and can be neglected. The simplest amplitude modulated pulses are Gaussian pulse, sine pulse or sine-square pulse [1]. The main drawback of these simple shapes is that they produce a phase gradient over the excitation bandwidth and their excitation profiles are non-uniform over the bandwidth of interest. The amplitude modulated pulses can easily be shifted off-resonance by applying a phase ramp over the pulse according to equation (4). 

Fig. 5.3.5 [Cal2] The sine pulse, (a) The amplitude of the rf carrier is modulated by a truncated sine function, (b) The magnitude of the Fourier transform of the pulse is a rectangular function distorted by wiggles in the centre and near the edges.

Apart from the gradient itself, the degree of suppression is related to the efficiency of excitation by the selective pulse and thus the choice of selective pulse is important with, for example, hyperbolic secant pulses perform better than sine pulses." If the solvent Ti is very short and on the order of the time for the dephasing procedure, then some (unwanted) z-magnetization will be re-established prior to the excitation pulse. One method of circumventing this... 

Figure 5 Examples of the frequency profiles of a SECH pulse and a three-lobe sine pulse. The SECH pulse has far less prominent side-bands than the sine. The profiles were generated on a 2.4T Bruker Avance Scanner at University College London.

The ovCTall maximum response is the larger of the two maxima determined separately for the forced and firee vibration phases. Fig. P4.19c shows that if td > Tn, the overall maximum is the largest peak that develops during the force pulse. On the other hand, if td < Tn, the overall maximum is given by the peak response during the free vibration phase. For the special case of td = Tn, as mentioned earlier, the two individual maxima are equal. The overall maximum response is plotted against td/Tn in Fig. P4.19d for each td/Tn it is the larger of the two plots in Fig. P4.19c. This is the shock spectrum for the full-cycle sine pulse force. 

Determine response to half-cycle sine pulse. 

Initially RF pulses such as sine pulses (with trapezoidal gradients) or high-order sine pulses (with sinusoidal gradients) were used. Now much more sophisticated complex pulses (i.e. containing real and imaginary profile information) are used to obtain better and more exact slice selection. 

The acceleration-time history is considered to be the primary description of a shock motion. Various types of shock motions like acceleration impulse, half sine pulse of acceleration, decaying sinusoidal acceleration etc. are frequently encountered in practice. The time histories of velocity and displacement are derived from basic acceleration-time history by integration. 

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