What does all of this mean to the measured MRI ``signal''?

• ``signal'' that we measure is actually the product of the real signal and 2 other functions representing the effects sampling and truncation
  

  $${\rm s}_{m}(k) = s(k) \cdot u(k) \cdot {\rm rect}\left( \frac{k+\frac{1}{2}\Delta k}{W}\right)$$

  $$= \Delta k \sum_{p = -n}^{n-1} s(p\Delta k)\delta(k - p \Delta k)$$ (10.11)

  
  

• This will have profound effects on the images that we measure. (please record your informed speculation here)

  
  
  
  
  
  
  
  

• Finish up with Fourier transform concepts by introducing a discrete Fourier transform which is natural progression from finite sampling. Want to map N sampled points in one space to N points in inverse space.