I can't explain why this is occurring on both front and back, but I had the exact same symptoms on my front brake only. In addtion to some of the checks already mentioned, I gave the rim a very thorough cleaning with alcohol and cleaned and roughed up the brake pad surface. Note that this didn't work the first time, so I filed more off the pads...and this time it fixed the problem. Apparently there was one point on the rim that the pad was "grabbing" differently causing exactly the noise you describe with each revolution.