My situation is similar to having a Cos and Sin function that would be combined with the envelope profile, but the envelope is offset horizontally by some dt.

It would be something like a*Cos (t + dt) + b*Sin (t + dt) = Over (t), I want to find the coefficients and the time change {a, b, dt}.

I have 2 datasets (lists) for the two input datasets and the dataset for the envelope. How can I fit this? The use of a NonLinearModelFit cannot be adjusted to so many functions at once.