Note that (frequency)=(speed of light)/(distance between subsequent pulses). Clearly the frequency and the speed of the light pulses vary proportionally for the receiver.
John Stachel: "But this seems to be nonsense. How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam? Einstein states that he wrestled with this problem over a lengthy period of time, to the point of despair." http://www.aip.org/history/exhibits/einstein/essay-einstein-relativity.htm
"Seems to be nonsense" is a euphemism. Einstein's constancy of the speed of light, the linchpin that holds the whole range of modern physics theories together, is OBVIOUS NONSENSE.