To my understanding the Relativistic Doppler shift is a product of the classical velocity shift and the dilation factor arising from that velocity. The classical effect can be red or blue depending on whether the emitter and receiver are receding or closing respectively. The dilation factor in both cases effects a red shift offset. SO in closing the net effect can be blue shifted but it will be blue shi8fted less than the classical value by the gamma factor. In the case of light emission I understand it as a decrease in electron resonance frequency due to time dilation. So in one frame A we can say that signals received from B are red shifted by the additional gamma factor because the emitting electrons were time dilated and therefore emitted photons of a lower frequency. But if we consider signals sent from A to B from frame A we cannot say the signals will be red shifted when received in B because the electron frequencies in B are relatively dilated. If this were the case the result would be a blue shift in addition to the classical effect not the expected red shift. As far as I can see it necessitates an assumption that the dilation occurs in the emitter frame but does not apply to the receiver. In effect a preferred frame. Is there something simple I am not getting here?