title: Generate random numbers with specific Fourier spectrum
body: <p>I have a set of random numbers that will be used for a simulation. However, I need this numbers to have a specific Fourier spectrum (that looks similar to the real data I have) but without changing the phase of the random numbers.</p>
  
  <p>Does anyone have any idea on how I can use the amplitude of the Fourier transform of the real data to generate approximately similar Fourier spectrum for the random numbers? </p>
  
  <p>What I thought of doing is:</p>
  
  <ol>
  <li><p>Take the Fourier transform of the real data.</p></li>
  <li><p>Multiply the spectrum (|F(<em>w</em>)|) of the real data by the Fourier transform of the random numbers.</p></li>
  <li><p>Calculate the inverse Fourier transform of the multiplied signal to get the random numbers.</p></li>
  </ol>
  
  <p>Would this approach work well?</p>
  
  <p>What would be the effect on the phase angle (if any)?</p>
  
  <p>Any suggestions on different ways to do that are welcome. </p>