I was aware that skewed Gaussian you can get by convolving an exponent, Heaviside function and a Gaussian ... so I imagined that probably you would be able to separate them by the reverse process, namely deconvolution. I was thinking about one particular project then, but just now, I realized ... what would happen if I apply the same idea to spectra from nuclear experiments ...
It is pretty well known that scintillation detectors are not so big on resolution, they have nice wide peaks, which accidentally are Gaussian functions. So my mind went on wandering ... if I assume that peaks are in reality delta functions, and they are convolved by a Gaussian, generated from the acquisition system, we would get what we see in the spectrum. But then ... if one applies a deconvolution method in some manner, in theory it is possible to separate every single peak ...
Here it goes a little bit of mathematical motivation, but the idea is sound, at least for now. When I have the time I will implement it, and report the result.
Lets say that you have two functions, their convolution is defined by:
This is just a definition of a functional, and it has some cool properties, but most importantly the following two:
The first is just identity equation, where delta is the delta function (no surprise here). The second one is called the convolution theorem, Where F{} is the Fourier transform.
To keep this short I'll only provide a guideline to the remainer of the method proposed. Let's say we have a system of the type:
The filter itself may not be in the frequency domain, which is the point of the whole post. It can be created in such a manner, that it's just applied to the spectrum to enhance resolution. The idea can be implemented through the Wiener deconvolution process.
A am far from the idea, that one could get real delta functions, but decrease in the dispersion of existing Gaussian peaks, would be more than enough. So far this is just my imagination going wild, but still it has some potential.
