Tweet
Jesus Dapena noted that collecting extra data does not help for Vaughn's
example of dropping an object or for impacts. He is absolutely correct.
The issue here is that all smoothing algorithms make some assumptions about
the data, especially about its continuity and have serious problems with
discontinuities. In the case of a dropped object, the second derivative is
not zero at the ends, just at it does some extreme things with an impact.
You cannot apply a smoothing algorithm _through_ an impact, no matter what
order you use (and you dont want to). There is no algorithm for which you
wont find examples of boundary conditions that cause it to generate
misleading results. This is not a case of garbage in, garbage out. Cubic
and quintic splines both work well when used properly and distort the data
when not. It's just that there is no substitute for collecting and
analyzing data thoughtfully.
__________________________________________
| Gerry Gottlieb (617) 353-8984 |
| NeuroMuscular Research Center 353-9757 |
| Boston University fax 353-5737 |
| 44 Cummington St. |
| Boston MA 02215 /\ |
|_______________________/\ / \ /\_______|
| \/ \/
example of dropping an object or for impacts. He is absolutely correct.
The issue here is that all smoothing algorithms make some assumptions about
the data, especially about its continuity and have serious problems with
discontinuities. In the case of a dropped object, the second derivative is
not zero at the ends, just at it does some extreme things with an impact.
You cannot apply a smoothing algorithm _through_ an impact, no matter what
order you use (and you dont want to). There is no algorithm for which you
wont find examples of boundary conditions that cause it to generate
misleading results. This is not a case of garbage in, garbage out. Cubic
and quintic splines both work well when used properly and distort the data
when not. It's just that there is no substitute for collecting and
analyzing data thoughtfully.
__________________________________________
| Gerry Gottlieb (617) 353-8984 |
| NeuroMuscular Research Center 353-9757 |
| Boston University fax 353-5737 |
| 44 Cummington St. |
| Boston MA 02215 /\ |
|_______________________/\ / \ /\_______|
| \/ \/