This question has been around for a while,so here's my 2 cents.When converting AC to DC using a full wave bridge,you have 2 diodes on that are conducting and the other 2 that are not conducting,then the AC changes this yields a positive dc and a negative dc,now anytime you turn on and off a diode it has a time period to be fully on or fully off,when you place a small cap across each diode it helps smooth that out,this Idea is to remove it with a small cap,this also make noise riding on the dc,The big cap smoothes some of this out also,
The transformer also contributes to this problem of turning the diodes on and off because the secondary is ringing,so the on off signal that we want to get rid of is turning the diode on and off just a little bit,now what fixes almost all of this is a snubber (look for quasimoto)It shows how to adjust the ringing with a circuit that connects to a oscope.
It tames ringing to almost nothing,before it gets to the bridge diodes,so it take less capicatance to get a almost flat DC and your diodes can do a better job!