An alternative derivation of Einstein's Doppler shift and aberration formulae

I propose an alternative, purely kinematical, derivation of Einstein’s Doppler formula. It is valid for periodic signals of any shape that propagate with the velocity of light. The formula is asymptotic in a parameter proportional to the relative variation of the distance source-receiver during one period. As a by-product, I also derive an alternative proof of Einstein’s aberration formulae.