http://www.youtube.com/watch?v=SC0Q6-xt-Xs "Doppler effect - when an observer moves away from a stationary source. Pay attention to the velocity of the wave relative to the observer. When an observer moves away from a stationary source, the period of the wave emitted by a source is longer and the observed frequency is lower. Because the velocity of the wave relative to the observer is slower than that when it is still."
The observer starts moving away from the light source with speed v. The frequency he measures shifts from f=c/d to f'=(c-v)/d, where d is the distance between the pulses. (If v is small enough, the formula f'=(c-v)/d is virtually exact no matter whether the classical or relativistic Doppler effect is considered.)
The speed of the pulses relative to the moving observer is:
c' = d*f' = c - v = c
where c - v = c is the fundamental equation of special relativity: