Compare the ingestion of a light signal sent from the rocket, if:
a) the rocket moves away from the observer,
b) the rocket is approaching the observer.
The speed of signal propagation does not depend on the speed of a rocket and is equal to the speed of light, that is why the time will be the same. In cases a) and b) the frequency of the received signal will vary - if the rocket moves away the signal will be weaker (red Doppler shift), with the approach of the rocket the signal will be stronger (purple).