Agilent Technologies ESA Series User's/Programmer's Reference page 377

Figure 5-2 Smoothing With 401 Trace Points and 31 Smoothing Points
Chapter 5
Increasing the number of points increases smoothing at the cost
of decreasing resolution.
The amount of smoothing decreases at the end points. Because
:TRACe:MATH:SMOoth <trace> averages values that occur
before and after the data point in time, display irregularities can
be caused at the start and stop frequencies. To avoid possible
irregularities (signal distortion) at the ends of the trace, use
small values for the smooth parameter.
Refer to Figure 5-2 for a discussion of this end-point smoothing
phenomena. With 31 smoothing points and a 401 point trace,
point 16 will be the first point to have full 31-bucket smoothing.
Likewise, point 385 will be the last point with full 31-bucket
smoothing. Under the conditions stated, points 2 through 15 will
be smoothed as follows: Point 2 is derived from averaging
buckets 1 through 3. Point 3 is derived from averaging buckets 1
through 5, Point 4 is derived from averaging buckets 1 through
7, and so forth until point 16 is reached. The quantity of buckets
used for the smoothing running average increases at the rate of 2
buckets per point, from point 1 to point ([smoothing number/2]
+ 1), at which time the full number of smoothing points is
utilized. The same characteristic occurs at the completion of the
trace, beginning at point 386, when the number of averaging
buckets begins to decrease until point 401 is reached.
Remote Command Reference
TRACe Subsystem
377