I'm new to this, but I'm creating a simply background image for the header on my website. When I add a filter to the image, there is "white space" around the visible image which shows up when I export it (to convert to PNG). I'm trying to find a way to get rid of this white space. Not sure if that makes any sense, but advice would be appreciated.

Use the CLIP feature to get rid of the area you don't want to show

http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Clip.html