Sampling of k space

However, in order to be able to apply the inverse Fourier transformation, we need to know the dependence of the signal not only for a particular value of k (one gradient pulse), but as a continuous function. In practice, it is the Fast Fourier Transform (FFT) that is performed rather than the full, analytical Fourier Transform, so that the sampling of k-space at discrete, equidistant steps (typically 32, 64, 128) is being performed. 

In all of these exercises, be careful to consider aspects of numerical convergence related to the number of surface layers, the sampling of k space, and the like. As you gain experience from the first few exercises, fewer calculations to test convergence will be needed in the later calculations if you can clearly explain how the convergence information developed in the earlier exercises is relevant for the situations in the later exercises. 

In practice, the sampling of k-space takes place as we sample the NMR signal at successive time intervals along the time axis of data acquisition. Substituting kx = y Gx t/(2m) and (% =y Gx x/(2m), kxx=toox. Hence equation (10) is rewritten as... 

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