My .eps Vector Graphic needs a Quick Touch-Up

Hi. Illustrator abilities needed. I have attached my vector graphic containing a signature and a description. When zooming in, an unclean lining in almost the entire signature is clearly visible. The lining throughout is somewhat angular/cornered and all in all somewhat disharmonious. The quick work i need done is the following: -The "J" in the signature needs to be a bit larger (to fit the rest of the signature). -The lining of the complete signature has to be made into cleaner curves (the "J" and "L" are especially unclean), to give the signature a more professional look. -The description underneath should be centered. -No color changes. -Background transparent. -Needed as modifiable .eps file For someone who knows their way with Adobe Illustrator, this should be a quick and easy task. As you can see, i simply need a fining of the signature, making it look more graceful and professional. Thanks.