XMM-Newton Science Analysis System


asmooth (asmooth-2.29) [xmmsas_20141104_1833-14.0.0]

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Ways of specifying the convolvers

In all the following descriptions, the convolving function is designated by $c_{x,y}$, where $x$ and $y$ are integer pixel numbers. Convolvers must necessarily be of finite extent, hence are only defined over a rectangular array.

It is necessary to have some way to determine the `phase' of any convolver: ie, which pixel of the convolver array should be taken to have row and column indices $y$ and $x$ equal to zero. The rule applied by asmooth is as follows. If the convolver has for example $N$ rows, then row 1 plus the integer part of$N/2$ is taken as the zeroth row. This means that if $N$ is odd, the central row is the zeroth row, ie the row indices are taken to extend from $-(N-1)/2$ to $(N-1)/2$; if $N$ is even, the row indices run from $-N/2$ to $N/2-1$. The same rule is applied to the columns.