In the 47-page document posted on attorney Howard Kurtz's website Tuesday, the appeal brief cites three issues with Cooper's trial.
Cooper has been in jail since October 2008, when he was charged with murdering his wife. In May 2011, a jury found Cooper guilty of first-degree murder. He was sentenced to life in prison without parole.
Nancy Cooper, 34, disappeared on July 12, 2008. Her husband said she went out for a jog and never returned. Her body - clad only in a sports bra - was found in an unfinished Cary subdivision less than three miles from the couple's home.
Prosecutors said Brad killed Nancy because he was angry she planned to divorce him and move with their two daughters to Canada.
But Cooper's lawyers said he was innocent and characterized the investigation by the Cary Police Department as inept. They said detectives focused on Cooper from the beginning of their investigation and never looked at other suspects.
In the appeals brief, the defense takes issue with expert testimony given during the trial, as well as the state's investigation into Cooper's personal computer.
During the trial, prosecutors said Cooper planned his wife's death in advance, citing an analysis of Cooper's home computer that shows someone viewed a Google Earth map of the site where his wife's body was found the day before she disappeared.