The car makes this popping noise from one of the exhaust pipes. It sounds almost like a cammed piston engine without any sort pattern. It only comes from the right side. It pops louder after revving while the engine deaccels. Accompanied by a little white smoke at higher RPM's, but from both sides.(I've read that's normal?)
The car sat for a year before I bought it. It got stuck in reverse, kid thought it needed a trans, and after unflooding it there is seemingly nothing wrong with it.

 

Check your compression, sounds like you got a rotor with a dieing face

 

Thanks, the video is of the car in question. I'm currently trying to find a compression tester to use.

 

my car does that too. but it shoots fire at the same time. lol it sounds like its just back firing. check the plugs, check timing and check for vacuum leaks

 

What exhaust are you running on that car?
Is the CAT still on the car?..straight piped?...header?...

 

Mine did that before the dashpot was adjusted (the popping on decel). If it still popping at idle (hard to tell from video), I second the timing recommendation.

 

sounds pretty typical for a rotary engine, but your idle is high and so your timing isn't retarding during idle mode which would smooth out the idle. the dashpot as mentioned used to slow the throttle closing should help the decel pops.

 

As far as I know it's stock exhaust. The only thing I see aftermarket is a spongy air filter. I was under the car, doing the "screwdriver" trick, and everything looked original. Though, it's also the first rx7 I've been under.
I'm researching how to check the timing now, also.

 

My car would only pop a single time after a high rev. I second the compression and timing test. Also if the white smoke ever becomes excessive (only on engine start-up) then you've broken a coolant seal. Which would call for an engine rebuild, what I saw in your video looks pretty normal.