How to apply a text filter statically

Is there a way to apply a text filter (like Filtered HTML) statically, so that the filtered result is written to the database instead of the original contents?

Example:
I'd like to replace all links / source references of downloadable files and images with a file id.

From <a href="http://www.mydomain.org/files/mydocument.pdf">My Download</a>
To <a href="http://www.mydomain.org/my_module/13">My Download</a>

It would be nice to have the filtered code written to the db instead of the original code in order to keep my file management consistent.

Any idea how to do that?