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Did you have your iphone to sync with a email account (outlook, gmail etc.), they should be in there if you did.
If you didn't then there are various utilities to extract them from the backup file but having never used any of them I wouldn't know which one to recommend. Just try googling recover contact from iphone backup to find a few ideas.
On a Mac: ~/Library/Application Support/MobileSync/Backup/
On Windows XP: \Documents and Settings\(username)\Application Data\Apple Computer\MobileSync\Backup\
On Windows Vista and Windows 7: \Users\(username)\AppData\Roaming\Apple Computer\MobileSync\Backup\
then use any of database programmes to read the .db files. I personally used SQlite Database Browser 2.0 (please note I used this on my mac and can't remember if there is a windows version-but there are loads of other Windows programmes) and from there you can import into a .csv file and read in excel (more detailed instructions can often be found on the sites of such programmes, sorry, I am typing this from the top of my head, hence no further detailed instructions)