It happens to all of us. Someone sends us an old logo and asks us to update it, re-size it, create a print version, etc. and all they have is a JPG or a scanned image. That used to drive me crazy because I knew that I’d have to spend quite a bit of time tracing the image and cleaning it up, before I could create a clean vector image but no more.
Inkscape to the rescue! Inkscape is an open source scalable vector graphics editor with capabilities similar to Illustrator, CorelDraw, or Xara X, using the W3C standard Scalable Vector Graphics (SVG) file format.
Inkscape.org has the download, FAQ, documentation, etc. but the steps below should get you through the scenario I mentioned.
Download and install Inkscape. The blank screen looks like this:
Save the file as a .svg. .png, *.ai (for Illustrator). You now have your logo in vector (eps) mathematical format resulting in the best results for images large and small with no loss of definition (i.e. a small logo can now be mathematically re-sized to create a banner and still be just as sharp as the original. And Inkscape made it a fairly painless process.
As with all open source software, if you find that it helps you, then consider making a donation on the Inkscape organization website.