Non-stationary signal decomposition

suppose f(t) is a non-stationary signal which can be expressed as follow:

f(t) = A1(t)*sin(w1*t) + A2*sin(w2*t) + ... + An(t)sin(wn*t), where 0<= t <= td.

How can I find each Ai corresponding to circular frequency wi?

Is there any MATLAB function which can be employed for this purpose?

emd function decompose a signal to its intrinsic mode functions (IMF) and each IMF has the same length as original signal. I am looking for something like emperical mode decomposition but it should be capable to extract A1, A2, ..., An.