Second Battery?

I've got an '04 Supra Launch SS and my amp cuts on and off at random times. My system includes: the stock Kenwood deck, 1000 watt 4-channel Kicker amp, 12" Kicker L7 sub, and '04 fusion t-series 3-way tower speakers with 4 gauge Stinger power and ground wire. The front channels push the tower speakers and the rear channels are bridged to push the sub. I've bought a 1 farad capacitor that I am going to install this year, but I don't know if that is going to be enough. Do I need a second battery and if so, what kind should I get and how do I hook it up to the other battery that is already there?