# @SBX, @SBN : smoother

#### 2.4.10 @SHF:n–shift

The transformation @SHF shifts the data up or down in subscript by the number of points given as the argument.

Examples:

```
u[L=@SHF:2]```

associates the value of U[L=3] with the subscript L=1.

```
u[L=@SHF:1]-U```

gives the forward difference of the variable U along the L axis.

#### 2.4.11 @SBX:n–boxcar smoother

The transformation @SBX applies a boxcar window (running mean) to smooth the variable along the indicated axis. The width of the boxcar is the number of points given as an argument to the transformation. All points are weighted equally, regardless of the sizes of the grid boxes, making this transformation best suited to axes with equally spaced points. If the number of points specified is even, however, @SBX weights the end points of the boxcar smoother as 1/2.

Example:

```
yes? PLOT/X=160W/Y=0 u[L=1:120@SBX:5]```

The transformation @SBX does not reduce the number of points along the axis; it replaces each of the original values with the average of its surrounding points. Regridding can be used to reduce the number of points.

#### 2.4.12 @SBN:n–binomial smoother

The transformation @SBN applies a binomial window to smooth the variable along the indicated axis. The width of the smoother is the number of points given as an argument to the transformation. The weights are applied without regard to the widths of the grid boxes, making this transformation best suited to axes with equally spaced points.

Example:

`yes? PLOT/X=160W/Y=0/Z=0 u[L=1:120@SBN:15]`