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You may not believe this but this problem could be caused by a bad alternator diode (excessive AC ripple). Please do yourself a favor and eliminate a charging system problem before performing any additional repairs.

Howto perform charging system voltage drop test

Note to the doubters. The excessive AC ripple can "fool" the cam sensor. What's one possible "cause" for back fire? How about unstable timing. What's one possible cause of unstable timing? How about an unstable cam sensor? Do you see where this is going?

Want more information? Do you have an ODB2 scanner? If you did you could monitor timing advance while this problem is happening. Here's some information on an affordable Windows unit.

ForScan ODB2 scanner w ELM327 USB

ForScan ODB2 scanner w ELM327 USB

While working on your car have you ever wanted: to find an ODB2 operational PID value (say fuel pressure or MAF)? How about graph a PID value over time? Or compare multiple PID's over time? Access a bi-directional PCM control such as test a...

www.stangnet.com

@wmburns I would advise to follow burns suggestions. On a side note; Popping in the exhaust can be a couple different things. Excess fuel being burnt in the exhaust is the sound your hearing when it randomly pops. Possible causes below.

-An injector failing becoming stuck open and injecting too much fuel that isn't getting burnt up during the compression cycle.
-A vacuum leak commands the PCM to add more fuel since more air is entering in to the combustion cycle, too much fuel and some of it may not ignite during the compression cycle
-An exhaust leak before your oxygen sensors will cause the oxygen sensors to misread and tell your PCM to add more fuel when it doesn't need too
-faulty oxygen sensor on bank 1 or 2 and on your downpipe. Could be any of the 4 that is bad.

All of these can be possible causes for the backfiring
I'd suggest to pull codes if you have any and start there. I've personally experienced a bad oxygen sensor before and had the same issues but that may not be your issue.