I am trying to find a value from a given mathematical function whose input is supposed to be derived from FFT components. Essentially, I follow the procedure from  which assumes that a given sine wave (regular wave) is composed of a cosine and sine wave of different amplitude but the same frequency.
How can I find the amplitudes of each decomposed wave if the FFT shows just one peak at the wave frequency?
The signal is a regular sine wave superimposed with 2 waves traveling in the opposite direction. We have two singals (i.e. two measurment devices) whose components are required for the mathemtical equation. So,
Signal1 = Wave1 + Wave2 = a1cos(kx-ft+e1) + a2cos(kx+ft+e2) = A1cos(ft) + B1sin(ft)
Signal2 = Wave1 + Wave2 = a1cos(kx-ft+e1) + a2cos(kx+ft+e2) = A2cos(ft) + B2sin(ft) where,
- a = ampltiude
- k = wavenumber
- f = frequency
- e = phase
- t = time
The paper states A1,A2 ,B1 and A2 can be estimated through Fourier Analysis to be plugged into a equation.