
#include <nagmk26.h>

$$\mathrm{Data}=\mathrm{Smooth}+\mathrm{Rough}\text{.}$$ 
1.  4253H,twice consisting of a running median of $4$, then $2$, then $5$, then $3$ followed by hanning. Hanning is a running weighted average, the weights being $1/4$, $1/2$ and $1/4$. The result of this smoothing is then reroughed by computing residuals, applying the same smoother to them and adding the result to the smooth of the first pass. 
2.  3RSSH,twice consisting of a running median of $3$, two splitting operations named S to improve the smooth sequence, each of which is followed by a running median of $3$, and finally hanning. The end points are dealt with using the method described by Velleman and Hoaglin (1981). The full smoother 3RSSH,twice is produced by reroughing as described above. 