2002 Mitsubishi Galant Rough Idle

When I first start the car in the morning the car runs real rough. When I start backing out, the engine hesitates and sputters like its going to stall. When I move forward and depress the gas pedal it does the same thing. At first going down the road it acts in the same manner. But all this only lasts for about 2-3 minutes then it runs normal the rest of the day. My mechanic does not know whats wrong with it either, and he is pretty good at what he does, but this one is a mystery to him as well.