I've tried searching on google (rx8club.com (issue) but I couldn't find anything on it. I saw a couple issues that sounded similar but as I read on it wasn't the same issues.

2004 4speed AT

So the issues start about a week or two after I replaced the engine, which was about six months ago. So as I was pulling into my driveway and was about to put it into park there was a sound that came somewhere from the engine area. It was like an exploding or a popping sound. Like a little boom. Ever since after that, every time I accelerate from 2 to 4 RPM it'd make a stuttering sound like a harley motorcycle (like putt putt putt and it's quite loud). It also happen in neutral and park too, it's just not as loud and you can only hear it if you listen closely.

took it back to the dealer they said it was my spark plug wires, so i paid them to replace that, still didn't fix the sound. took it back to them again, they said it was my catalytic converter, replaced it with a whole new exhaust system and it still didn't fix the sound. One of the worse dealership I've ever had to deal with... so that lead me here to search for the issue and troubleshoot.

There is no lost in power that I'm aware of. I was told that it could be my header gasket? But I'm not too sure.