Selective rectangular pulse

The peak rf amplitude required to achieve optimum excitation with a selective excitation pulse is given in comparison to the rf amplitude required to achieve an on-resonance 90° flip-angle with a selective rectangular pulse, the simplest conceivable shape. 

The principle of multiple selective excitation has been incorporated into a few ID and 2D experiments, the schemes of which are shown below (fig. 1). Depending on the experiment, either a DANTE pulse train (ID TOCSY [2]), frequency selective 180° pulses (ID NOE [3], ID INADEQUATE [4], ID C/H COSY [5] and 2D TOCSY-COSY [6]) or frequency selective 90° pulses (2D HMBC [11]) are applied to selectively perturb and uniquely label selected spins. Besides the DANTE pulse , composed itself of a series of non-selective rectangular pulses, Gaussian-shaped 180° and... 

Fig. 1. Computer simulations of four selective excitation pulses. (Top) Pulse shapes. From left to right 90° rectangular pulse, 270° Gaussian truncated at 2.5%, Quaternion cascade Q, and E-BURP-1. The vertical axis shows the relative rf amplitudes, whereas the horizontal axis shows the time. (Middle) Trajectories of Cartesian operators in the rotating frame...

As long as the boundary and initial conditions remain unchanged, the band profiles on the reduced time and length scale depend only on the column efficiency. The conventional boundary and initial conditions for all modes of chromatography state that (1) the column is equilibrated with the mobile phase prior to the beginning of the separation (2) the sample is then injected as a rectangular pulse and (3) the separation proceeds as required by the specific mode selected. The amount of sample injected is determined by the volume and the concentration of the feed injected. As long as we avoid serious volume overload, the actual values of these two parameters are immaterial. Only their product, i.e., the amount injected, will influence the band profile. 

This mass separator is a new type, especially accommodated to be compatible with the 2V2-D geometries available in this fabrication process. The synchronous ion shield (SIS) analyzer selects the mass, for which the filter is transparent, by a traveling high frequency rectangular pulse stream (rise and fall time <1 ns) of a swept frequency (0-270 MHz), which is supplied to a comb shaped electrode arrangement. 

Shaped pulses are created from text files that have a line-by-line description of the amplitude and phase of each of the component rectangular pulses. These files are created by software that calculates from a mathematical shape and a frequency shift (to create the phase ramp). There are hundreds of shapes available, with names like Wurst , Sneeze , Iburp , and so on, specialized for all sorts of applications (inversion, excitation, broadband, selective, decoupling, peak suppression, band selective, etc.). The software sets the maximum RF power level of the shape at the top of the curve, so that the area under the curve will correspond to the approximately correct pulse rotation desired (90°, 180°, etc.). When an experiment is started, this list is loaded into the memory of the waveform generator (Varian) or amplitude setting unit (Bruker), and when a shaped pulse is called for in the pulse sequence, the amplitudes and phases are set in real time as the individual rectangular pulses are executed. 

Such excitations have been called shaped pulses, and a considerable effort has been expended in an attempt to optimize their shapes. A simple Gaussian shape is a considerable improvement over a rectangular pulse, but is not entirely effective in achieving an optimal peak shape. The use of more elaborate mathematical functions improves the shape of the signal, although with increasing loss of intensity. The BURP Band selective. Uniform Response, Pure phase) family utilizes an exponentially dependent sinusoidal series of Gaussians with considerable success in a variety of situations (EBURP for REBURP for 180 ). 

A single RF pulse is sufficient to create MQC in half-integer quadrupolar spin systems, as long as the strength of the RF pulse Pj < vq, which is often the case. Similarly, a single RF pulse can also convert the MQC to observable SQC. We denote such a basic sequence as Ph- h which is sketched in Fig. 5a, where Ph denotes a hard unmodulated rectangular pulse often called CW pulse. The first pulse is optimized to excite MQC and has a phase ]. The second pulse with a phase converts MQC to SQC which is detected by the receiver. The receiver phase ec is cycled to select the required coherence pathways and to eliminate the undesired ones. The value of the receiver phase equals — [, Ap,,] where Ap,- is the difference between the coherence order after and... 

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... 

McCoy et a/. have proposed a method termed ERASER based on self-refocused and hard rectangular pulses. The scheme does not generate phase roll. Moy et alP have demonstrated the use of frequency shifted, self-refocused top hat pulses to observe amide resonances, that they termed selective-excitation-corrected spectroscopy (SelECSy). This method, although not providing exceptional water suppression, overcomes the dynamic range problem and produces uniform amide proton excitation... 

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