title: Deconvolution of data convolved by a Gaussian response
body: <p>I have a set of experimental data <code>s(t)</code> which consists of a vector (with 81 points as a function of time <code>t</code>).</p>
  
  <p>From the physics, this is the result of the convolution of the system response <code>e(t)</code> with a probe <code>p(t)</code>, which is a Gaussian (actually a laser pulse). In terms of vector, its FWHM covers approximately 15 points in time.</p>
  
  <p>I want to deconvolve this data in Matlab using the convolution theorem: <code>FT{e(t)*p(t)}=FT{e(t)}xFT{p(t)}</code> (where <code>*</code> is the convolution, <code>x</code> the product and <code>FT</code> the Fourier transform).</p>
  
  <p>The procedure itself is no problem, if I suppose a Dirac function as my probe, I recover exactly the initial signal (which makes sense, measuring a system with a Dirac gives its impulse response)</p>
  
  <p>However, the Gaussian case as a probe, as far as I understood turns out to be a critical one. When I divide the signal in the Fourier space by the FT of the probe, the wings of the Gaussian highly amplifies those frequencies and I completely loose my initial signal instead of having a deconvolved one.</p>
  
  <p>From your experience, which method could be used here (like Hamming windows or any windowing technique, or...) ? This looks rather pretty simple but I did not find any easy way to follow in signal processing and this is not my field.</p>