I have a 2005 Dodge Stratus that has a center dash speaker that I would like to incorporate into the new system. I've already purchased the Sony XAV-AX8500, an Infinity 3004 4ch amp, and Infinity Reference separates front and rear. Will I need to add a DSP? Change the amp? A wiring diagram would really help!
Shouldn't need a diagram. If you are powering the center speaker off the amp, just need to run the wires from the amp to the speakers. Easiest way to find the best wire routing path would be finding a YouTube video of your cat doing a similar install. If not, you'll have to do some experiments and find out the best paths.
The easiest and probably the way you should do it if you are wanting to use that speaker is just run your door speakers off the 4 channel amp and the the center channel just use the factory wiring. I can't imagine the center speaker is much bigger than a 2-3 inch speaker so head unit power should be more than enough given how easy full range speakers are to drive
Personally, I'd just ditch the center channel all together. It will mess with the soundstage and since you are replacing the speakers with components they will have crossovers to split the frequencies to the respective speakers. The center channel stock is likely just to pick up on mid and high frequencies while your door and rear deck speakers pick up mid bass and lower
As for the DSP, it'll depend on how you listen to your music. If you stream Bluetooth from your phone or use AUX or USB to connect the radio, do yourself a favor and download Poweramp Equalizer. 32 band EQ so you can customize it extensively and also comes with a preamp gain boost as well. It's what I use and I love it.
Other than that, your head unit should have built in DSP and other settings. I've never used a Sony head unit so I'm not too sure how extensive the options are but I always opt for Kenwood and their range single DIN units for $120-140 have great DSP and time alignment settings built in.
Other than that if you are set on a DSP, check out NVX's. They have a digital EQ unit with all kinds of options for $160ish. You're not gonna find anything better than a dozen band EQ with little or no crossover settings for that price. But I'd say you shouldn't need one at all