Both sides are unbeaten in the pool ahead of Friday's meeting, with Edinburgh taking the top spot by virtue of a four-try bonus point picked up in last month's 11-try encounter with Racing Metro which ended 48-47.
Cardiff's impressive run of five consecutive wins in all competitions was interrupted last Friday as a weakened side were undone 52-9 by Leinster at the RDS.
This run, combined with an away victory over Edinburgh in the opening match of the RaboDirect PRO12 season, will no doubt fill the hosts with confidence ahead of this clash of capitals.
Edinburgh, however, have been increasingly impressive since an away win over Treviso sparked a similar run of form, stuttering against Munster away but returning against Aironi at Murrayfield last weekend in a 50-10 win.
Speaking at Wednesday's press conference, Bradley said: "Cardiff away will be a significant challenge indeed and is a match that will demand our utmost attention to every aspect of our game.
"We have a lot of respect for Cardiff, their players and the way they play the game. There is no hiding from the fact that they have a favourable position to ours in the RaboDirect PRO12 and have already beaten us at Murrayfield this season.
"However, we must have faith in our ability, something which has been gathering steam in the past six weeks.
"Our season has a degree of momentum to it, with the recent wins in the Heineken Cup and good wins over the Italian sides, home and away.
"If we maintain the consistency of these improvements in this double-header then we are capable of achieving our goal, which is to keep our place at the top of this group and qualify for the knockout stages of the competition."
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