XMM-Newton Science Analysis System


colsmooth (colsmooth-1.9.1) [xmmsas_20230412_1735-21.0.0]

Avoiding `droop' and filling in holes.

The weighting factor $G$ in equations 1 and 3 prevents ugly distortions of the smoothed output $y$ near the ends of the range of $y$ at $i=1$ and $i=N$. This treatment is also desirable near holes in the mask. To prevent this `droop' in the output close to holes, equation 2 is modified to the following:

$$F_{i,j} = \left\{ \begin{array}{ll} c_{j} \ x_{i-j} & \textrm{i... ...N]$\ and mask $m_{i-j}$\ is true}\\ 0 & \textrm{else}\\ \end{array}\right.$$

(The specifications for $G$ and $H$ should be amended in analogous fashion.) It should be pointed out that this cosmetic improvement is achieved at the cost of a little less noise suppression in these channels.

Similar costs are incurred by another appearence-enhancing feature of colsmooth, namely the ability to `paper over' holes in the mask which are significantly smaller than the width $M$ of the convolver. The size of holes to be interpolated is provided via the integer parameter fillholewidth. The interpolation is implemented by employing two different masks: let's us call them $m$ and $m^\prime$. The one ($m$) that appears in equation 3.3.1 and the analogous equations for $G$ and $H$ is left unchanged. The other ($m^\prime$), which appears in equation 4 and the analogous equation for uncertainties $v$, is for the most part set equal to $m$; the exception being within stretches of contiguous $m=false$ channels of length=fillholewidth: $m^\prime$ within such stretches is set to `true'. The result is that $y$ (and $v$) within these stretches or gaps is calculated as a weighted sum of only those values of $x$ that fall outside the gap. The results are acceptable provided the sum of those parts of the convolver that fall outside the gap onto the valid parts of $x$ is not too small a fraction of the total sum of the convolver.

Note that the default setting of fillholewidth=0 disables any hole-filling.