Fourier Transform Derivative Theorem

• By taking the derivative with respect to $x$ of both sides of the Fourier transform it is pretty easy to figure out the Fourier transform of the derivative of a function
  

  $${\cal F}\left(f^\prime (x)\right) = i2\pi kF(k)$$ (10.6)

  
  

• This makes it pretty easy to make a derivative image. Just multiply the k-space data by $k$, before taking the Fourier transform