Rectangular excitation profile

A sine-shape has side lobes which impair the excitation of a distinct slice. Other pulse envelopes are therefore more commonly used. Ideally, one would like a rectangular excitation profile which results from a sine-shaped pulse with an infinite number of side lobes. In practice, a finite pulse duration is required and therefore the pulse has to be truncated, which causes oscillations in the excitation profile. Another frequently used pulse envelope is a Gaussian frmction ... 

Figure 1.15 Time domain representation of a hard rectangular pulse and its frequency domain excitation function. The excitation profile of a hard pulse displays almost the same amplitude over the entire spectral range.

The shape of any rf pulse can be chosen in such a way that the excitation profile is a rectangular slice. In the light of experimental restrictions, which often require pulses as short as possible, the slice shape will never be perfect. For instance, the commonly used 900 pulse is still acceptable, while a 1800 pulse produces a good profile only if it is used as a refocusing pulse. Sometimes pulses of even smaller flip angles are used which provide a better slice selection (for a discussion of imaging with small flip angles, see Section 1.7). 

Hie selectivity of a rectangular RF pulse can be increased merely by lengthening the pulse and using a reduced power however, this approach is limited as it results in a sine function-shaped excitation profile. Also, to achieve the desired selectivity, the pulse duration will eventually become too long and solute and solvent relaxation effects may become significant during the pulse. Hence in attempts to keep the pulses short while retaining... 

Figure 9.10. Schematic excitation profiles for (a) a low-power rectangular pulse and (b) a smoothly truncated shaped pulse.

P = 1 kW at A. = 600 nm illuminates sample in a cell at p = 1 mbar and T = 300 K. A rectangular intensity profile is assumed with a laser-beam cross section of 1 cm. Which fraction of all IV,- in the absorbing lower level /> is excited when the laser is tuned to a weak absorbing transition /) k) with the absorption cross section... 

Figure 2. Time-domain excitation waveforms (left) and corresponding frequency-domain magnitude-mode spectra (right) of four excitation waveforms used in FT/ICR. A time-domain rectangular rf pulse gives a "sine" excitation spectrum in the frequency-domain. A time-domain frequency-sweep gives a complex profile described by Fresnel integrals. Single-scan time-domain noise gives noise in the frequency-domain. Finally, Stored Waveform Inverse Fourier Transform (SWIFT) excitation can provide an optimally flat excitation spectrum (see Figure 3 for details).

Nanowire profile also affects the excitation behavior of LSPs, i.e., it is one of the critical parameters that determine how electrons redistribute themselves in order to meet momentum matching condition. Effects of many profiles, such as rectangular, triangular, T and inverse T profiles, have been investigated [22, 23]. 

At potentials near the photocurrent onset (roughly Fn,), a spiked response is seen with a characteristic overshoot when the light is turned off. At positive potentials near the plateau regime (again for the specific illustrative case of an n-type semiconductor), the response reverts to a rectangular profile that mimics the excitation waveform. Intermediate response patterns manifest at potentials in between. 

Symmetrically shifted pulses have been proposed as a means of solvent suppression. Symmetrically shifted pulses are symmetrically shifted laminar pulses that contain equal numbers of rectangular pulse components of the same phase at an offset frequency. The basis of the symmetrically shifted pulse family is the SS pulse which is conceptually equivalent to applying simultaneous ir/2 rectangular pulses with two separate, but in-phase, transmitters at offset frequency from the water. On a practical basis an SS pulse is obtained by a complete Itt cosine modulation of a single transmitter (see Fig. 15). An S pulse is half of an SS pulse (i.e. a half-cycle tt pulse) which results in a narrower null and a 180° phase inversion at the transmitter frequency. They are also the soft, continuous equivalent of binomial sequences. The SS and S pulses have broader excitation maxima than the sinusoidal profile of the JR sequence. The method has maximal excitation at an offeet frequency of second-order U-shaped water suppression. The exdtation profile is related to the maximum amplitude modulation and can be determined by numerical evaluation of the Bloch equations. Hence a new pulse shape must be used for each excitation window. The SS pulses give better water suppression than the JR sequence, but at the expense of poorer excitation of resonances closer to the water. Also, there is no phase inversion at zero frequency. The S pulse gives better excitation near the water frequency but with less water suppression. 

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