wave separation Say there is a wave of sines and cosines. (<- one can think of Fourier theory.)
A) There is a wave that has the same frequency all the time. However, amplitude (- shape) of each period differs. Is it possible to separate this wave into combinations of waves that have the same amplitude for each wave?
B) Say there is a added combination of two waves that are same in frequency but different in amplitude. The amplitude of each wave is equal all the time. Can the signal be decomposed into two signals that were combined?
Thanks.

For A, what you probably mean by the same frequency all the time is that the wave passes through zeros (maybe also maxima) at the right time spacing.  It would be something like $f(t)=a_n\cos t$ where $a_n$ is the amplitude for period $n$.  This is a well defined function (given the list of $a_n$) but it has energy at frequencies other than $\frac 1{2\pi}$ as you can see from an FFT.  In particular, the derivative is not continuous when you change between the $a$'s
For B, yes, you can split out the time variation and use the usual formulas for the sum or difference of sinusoids
