its gonna sound different but im not sure what u mena by loud rumbling noise. What kind of intake did u install? also what year is ur car?

if it happens during deceleration (off the throttle but clutch out) it's probably running lean..although i would think your MAF should compensate for the increased air flow from your intake....first thing i'd check is your MAF

Yeah. Throaty, I think is the word you are trying to say.

apg, he made one.