Doppler Effect from a Transmitter in Translational Motion

The signal received at a ground station from a source in translational motion is investigated. The analysis is relativistically correct. Attention is focussed on the spectrum of the incoming signal. When receiver and transmitter are permanently activated, the spectrum is band-limited and shows two infinite peaks. The effect of a limited receiver turn-on time is analysed by multiplying the gain of the receiver with a time factor e-t 2/t 2o. The infinite peaks the spectrum disappear. To investigate the effect of the transmitter turn-on time, the spectrum of the signal received from an antenna activated by a sinusoidal current modulated by a Gaussian pulse is evaluated. This spectrum turns out to be a Gaussian pulse.