[From Bill Powers (2006.12.23.1930 MST)]
Martin Taylor (2006.12.23) --
I guess I was the one skipping steps this time. The phase angle between d and o, when d is a sine wave, is the angle between two rotating vectors in the complex plane. The complex plane, with k along the real axis and jw along the imaginary axis, is the basis space. So the phase angle I computed meets your definition of the correlation between d and o.