[CSC 335] Boxcar Filter

[Andrew J. Pounds]

  I got some questions this past weekend on boxcar filtering -- so I 
want to clarify some things.

There are TWO variables associated with the boxcar filter: size and passes.

For the purposes of this discussion lets imagine we have an array of 10 
elements with a boxcar size of five doing two passes.


There are multiple ways to implement the boxcar average -- but so we 
will all get the same (or similar results) lets standardize on one 
method that should give reasonable results without "end tail effects".


Here is my list of elements:

1
	2
	3
	4
	5
	6
	7
	8
	9
	10
273
	237
	302
	786
	1027
	635
	400
	370
	202
	250



Now -- with a boxcar size of 5 I could start in element 3, average 
elements 1-5, and replace element three by that value.  the problem is 
that if I apply such a filter several times the ends will tend to "tail 
up".  So, lets do the following.

The first element to be averaged will be the first element in the array, 
but the boxcar will only extend to the right (boxcar size)/2 -- so out 
to 3.  So the first element would be replaced by the average of elements 
1, 2, and 3.

After first operation the array looks like...

1
	2
	3
	4
	5
	6
	7
	8
	9
	10
271
	237
	302
	786
	1027
	635
	400
	370
	202
	250



In the next operation the center of the box slides one to the left so 
cell 2 is replace with the average of cells 1-4.

1
	2
	3
	4
	5
	6
	7
	8
	9
	10
271
	399
	302
	786
	1027
	635
	400
	370
	202
	250


In the next step the full "five sized" box is being used so 3 is replace 
by the average of 1-5

1
	2
	3
	4
	5
	6
	7
	8
	9
	10
271
	399
	557
	786
	1027
	635
	400
	370
	202
	250


The boxsize of 5 would then be used used until one got to element 8.  
After that element 9 would be calculated as the average of 7-10 and 
element 10 would be calculated as the average of elements 8-10.

If I did three passes then I would repeat this process three times.

Hope that helps alleviate any confusion.


-- 
Andrew J. Pounds, Ph.D.  (pounds at theochem.mercer.edu)
Associate Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627

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