Tomar un haz de partículas como un conjunto de muchas partículas. Suponga que dos variables aleatorias independientes $X_\beta$ $\delta$ que se suman a la posición horizontal $X$ de una partícula:
$$ X = X\beta + D_x \delta $$
($D_x$ is a simple number, the "dispersion" function in beam dynamics.)
I have a horizontal measurement of the beam profile, $f_X$, and another measurement of the longitudinal momentum profile, $f_\delta$. I have normalised both to unity area and take them to be measurements of the probability density functions of $X$ and $\delta$:
Now, I would like to determine the distribution / profile of $X_\beta$.
How do I have to proceed?
A first thought was to deconvolve $f_X$ with $f_{D_x\delta}$, after I interpolated both data sets to the same set of positions. Unfortunately, I failed with scipy.signal.deconvolve... I end up with an error quantity equal to the spectrum, i.e. I get nowhere.
If I convolve the two, I get an extension of $f_X$ by $f_{D_x\delta}$, as I'd expect:
(via numpy.convolve(f_x, f_Dxdelta, 'same') where both arrays have the same length and are w.r.t. the same positions)
I'd like to do the opposite now and 'remove' instead of 'add' the dispersive part. Or am I gone in the completely wrong direction?
One more possibly important information: I expect $X_\beta$ to have a normal distribution as opposed to $\delta$. I would like to extract the corresponding standard deviation of $X_\beta$ from $f_X$.
Gracias por tu ayuda, Adrian
PS: tengo la misma pregunta en la física de intercambio de la pila foro y me ha sido sugerido para pedir a la comunidad :-) ( http://physics.stackexchange.com/questions/224671/remove-measured-distribution-from-another-distribution )
