I have a set of experimental data `s(t)`

which consists of a vector (with 81 points as a function of time `t`

).

From the physics, this is the result of the convolution of the system response `e(t)`

with a probe `p(t)`

, which is a Gaussian (actually a laser pulse). In terms of vector, its FWHM covers approximately 15 points in time.

I want to deconvolve this data in Matlab using the convolution theorem: `FT{e(t)*p(t)}=FT{e(t)}xFT{p(t)}`

(where `*`

is the convolution, `x`

the product and `FT`

the Fourier transform).

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)

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.

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.