A problem could be caused by an engine performance problem; low compression in one or more cylinder, ignition misfire, or a vacuum leak.
A vacuum leak can show up as a rough idle and smooth out when the throttle is opened.
Another potential cause could be the pitching stopper. Has the starter been replaced or the transmission worked on before this problem surfaced?
(Note. The pitching stopper controls the stance of the engine/trans assembly and there is a Technical Service Bulletin out on the pitching stoppers if I remember correctly.)