show that an approaches 1/n, the filter-factor value for the equally-weighted case, and
the filter memory no longer fades. For values of F between zero- and one, the rate at
which the filter memory fades decreases as F increases. The analyst can control the rate
at which the filter memory fades by selecting an appropriate value of F.
As the number of points n increases, the value of an used in the recursive exponential-
filter equation decreases continuously as it asymptotically approaches 1-F. For any
given n, a larger an means more emphasis is placed on the current data point and less
on previous points. That is, the larger the recursive filter factor an, the faster the filter
memory fades. Filter factors for sample sizes up to- 300 points are shown in Figure 36
for six different filters. Early in the data-index count (n less than 30), the filter based on
index-number weighting has the fastest fading memory, since for 30 data points or
fewer the filter has the largest filter factors. After 160 points or so, the index-weighted·
filter fades at a slower rate than the exponential filter with F = 0.99. Consequently,
users of index-count-based fading filters frequently calculate a filter factor for some
maximum value of n that is then applied to all subsequent data points as well. For
example, if a maximum count of about 180 is used for n; this filter from _that point on
will behave similarly to the exponentially-fading filter with F = 0.99.

                          1 ---------------------------..-----,




                       0.1
           ...
           0
          ~
           ...
          LL
           Q)
          .:t:::
          u:::
           Q)
           >
          -~
                     0.01                                                                                                          ~
          .::S                                                                                                                 0
           i                                                                                                                   E
          a:                                                                                                                   Q)
                                                                                                                               E




                   0.001 ' - - - - - - - - ' - - - - - - ' - - - - - - - - - ' - - - - - ' - - - - . . . 1 . . . - - - - - - - '
                         0              50             100              150              200               250              300
                                              Number of Data Points in Sample

                          Figure 36. Recursive Filter Factor for Last Data P-oint


9/10/96                                                              94                                                                RTI