This is a question for the DIY And Advanced Projects section, but it would be my evaluation that you couldn't expect very deep output, or very much of it, without a ton of power or EQ. A subwoofer designed around a driver intended for hi-fi use (instead of car sound use) would be the best way to go. You should be able to sell that Alpine sub on eBay and get something out of it, which you could then apply toward your subwoofer project. If you've never attempted a DIY subwoofer project, you might be better served by a SVS, a HSU, or whatever other commercial products are being recommended these days.