Selective Pulses And Shaped Pulses

Because the excitation profile is the Fourier transform of the time course of the pulse, and because of the inverse relationship between time domain and frequency domain, a long enough pulse will lead to a very narrow sinc function. Figure 8.7 shows actual FT calculations done on rectangular pulse shapes. If we use a 90° pulse that is very long (e.g., 35 ms) and has very low power (3500 times lower amplitude or 12.3 x 106 times lower power than a 10 ^s 90° pulse), we will get a very narrow excitation profile (1/tp = 28.6 Hz). If we adjust the reference frequency so that one peak of interest in the spectrum is on-resonance (vo = vr), we could excite only the spins corresponding to this peak without affecting any of the other spins in the sample. This is called a selective pulse. The problem with the sinc function excitation profile is that there are many "wiggles" in the function that extend out quite far from the center of the spectral window. If another peak in the spectrum falls on the maximum of one of these wiggles, it too will be excited by the pulse, although the excitation will be weak.

How can we eliminate the wiggles? We could try other functions for the pulse other than the rectangular shape and think about what the Fourier transform is for these functions. A

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