Q: How do I authorize my computor to download previous purchases

On your Computer... Open iTunes...

and from the Menu Bar select Store...

From the Store menu, choose Authorize This Computer.

When prompted, enter your Apple ID and password, then click Authorize.

See Here >  http://support.apple.com/kb/HT1420

Download Past Purchases

1. Sign in with the Apple ID that you used for the original purchase. See which Apple ID you used to download an item.

2 )     See if the content is available for redownload. Previously purchased items might not be available if they're no longer on the iTunes Store