I have the Audio Controls LC6I and it's an In-Line Converter. A signal processor is just that - it processes the signal (the amp, the head unit will do that - OR, an aftermarket processor will, obviously, do it). The Audio Control unit one or two steps up from mine has a small modular unit that does just that...and you mount it somewhere in your car. It was an 8 channel unit (and if you want to keep your 8 speakers.....may be just the ticket).
I have 4 speakers, plus the sub (so I am wasting two of the '6' channels....but AC doesn't make a 4 - at least from what I could find). If your running a 5 channel JL amp and have 8 speakers - that's why you're not getting your oommph from the front doors. A 5 channel will run two fronts, two rears and a sub (if you read the specs, I bet you'll see the one channel geared to a 300 watt mono channel (or whatever wattage/power it is - for the low) and 4 channels to 100 watts (or whatever the wattage/power is - for the highs). Amps/converters can switch at what cut-off frequency you want to go to low and/or mid-high.
I run the JL 700/5 Amp and Focal's front/rear and a JL 10" sub. You can go eons beyond this of course, but it's clean, simple, great quality, and your ears bleed if you want. I like clean and clear.......and it fit my budget. Plus, this converter (at a small upcharge) had a small knob (mounted wherever you want) that controls bass/sub. I have it directly left/front of the cup holders on the center - between the parking brake and cup holders. Directly where my right hand would reach for. Dial it up or down depending on what's playing and my mood.....and for $30 bucks?......a no brainer. From a single 10"?? - I can only tell you - it works, and works clean and thumps well. And, no, I did not do the install, it was Car Toys and and I looked around - it was the 4th shop I went to. They were really good, a metro based place and the installer and head tech guy knew their stuff. The installer (all the installers) were like "oh, jeez......'Jim', you should see his house, it's a giant test shed of sound....." Who was I to argue? Install was clean and what I would have done - it was done in a working day - I did have to vacuum a bit.........no biggie.
So, if you want to bypass the amp and keep the function of the head unit (which I very much wanted to do), you need a seperate converter and amp - no question. If money is no option, then you can go amp(s), converter(s) - high and low, bigger subs, cleaner highs....again, sky's the limit.