Fourier Transform and digital sampling

As we have seen in the imaging sections the signal acquired in an imaging experiment is the spatial Fourier transform of the effective spin density. For this reason a deep understading of the Fourier transform and its properties is indispensable. Moreover, one should get an insight to the basics of digital signal processing, mainly discrete and finite sampling as in practice the acuired data is processed digitally and therefore these have to be taken into account. In the first part of this chapter the properties of the continuous Fourier transformation is presented followed by its discrete version and the effect of digital sampling.