Exact classical Doppler effect derived from the photon emission process
  The concept of photon is not necessary only applied to the relativistic Doppler theory. It may also work well for classical theory. As conservation of momentum and energy are physical laws, if applying these laws gives the exact relativistic Doppler effect, it should also give the exact classical Doppler effect. So far the classical Doppler effect is only obtained by using some approximation, as derived by Fermi in 1932. We show that the exact classical Doppler effect can be derived from the photon emission process in the exact treatment and reveal that these results are the same as those derived from the wave theory of light. 
Chyi-Lung Lin, Jun-Jia Pan, Shang-Lin Hsieh, Chun-Ming Tsai
physics.gen-ph