Property: Linearity in Fourier Transform:
The fourier transform of ax(t) is the integration of 1/T * (ax(t)*exp(-jwt))
The fourier transform of by(t) is the integration of 1/T * (by(t)*exp(-jwt))
The fourier transform of ax(t)+by(t) is the integration of 1/T * ((ax(t)+by(t))*exp(-jwt))
Because the linearity of the integral.
That is why the linearty in Fourier Transform.
