filter results on a json live search

General information for the website: ajax json live search wont filter results
Kind of development: Customization of existing website
Description of requirements/features: I have an form that does a live search with results with a json file so when i type in for example 'a' it brings up all the contacts in the address book but if I type a full last name for example if I type s-m-i-t-h it still shows all the contacts instead of the names that begins with s and then any name with smith in it. How would I be able filter these results ? If anyone can help me it would a massive help.
Similar urls: http://wsnippets.com/demo/bootstrap-live-search/
Extra notes: if its possible to have it done within 24 hours it would be a massive as I cant move on to the next parts before this is done.