I almost always use this power supply configuration, or a slight variant of this.
In my first trial, I had used AP7333-33 Regulator which was not able to supply adequate current to the Omega2.
Replaced this with the MIC5209-3.3V and everything was fine !
C4 need not be 1000UF, probably 100UF will also suffice.
C3 needs to be used if the Regulator is not near C2.
The MIC5209 may also be used after a 5V regulator like 7805.
I always use a full bridge rectifier circuit so that I can use virtually any type of Power Adapter.