### Filter Width box

The Filter Width value is an optional smoothing parameter for all of the filter types except the Spline filter. The value in this box determines the number of data points used for filtering to the right and to the left of each smoothed data point. For example, if the Filter Width value is m then the window is 2m * delta wide, where delta is the point spacing. The default value for this parameter is 3.

The value you type can be zero or any positive value.

- If there's no value at all (or if the value is zero), either the Cutoff Frequency or the Cutoff Wavelength value will be used to set the amount of smoothing.

- If either the Cutoff Frequency or the Cutoff Wavelength value is any non-zero, positive value, then the filter width corresponding to the cutoff frequency entered is displayed.

- If the Filter Width and the Cutoff Frequency or Cutoff Wavelength don't have values (or are zero), PC-DMIS will not filter the data.

The Filter Width value also determines how many points will be absent from the filter set when doing linear filtering. PC-DMIS removes those points that don't have enough data to the right or left to fill up the data window.

Note: A lowpass filter, one that filters out high frequency noise but transmits the lower frequency form and waviness, works by replacing the value at a data point by a weighted average of the values at a sequence of its neighbors. For the Gauss filter, for instance, the Filter Width specifies how many points to the left and right of a point are included in the weighted average. The weights (which are positive and add up to 1) are values of a Gaussian distribution function (also known as a Bell Curve). If the Filter Width is equal to m, then the smoothed point is at the center of 2m+1 points used in the weighted average. If the data is periodic, then the points wrap around and there are always enough points to the left and right of a point to compute this average. This is the case for a Polar filter. But for a Linear filter, the first and last m points do not have enough neighbors to compute the full weighted average, so these points are left out of the filtered dataset.