Doppler Radar - Police Radar GunDoppler radar works by sending a beam of electromagnetic radiation waves, tuned to a precise frequency, at a moving object. (You can use Doppler radar on a stationary object, of course, but it's fairly uninteresting.)
When the electromagnetic radiation wave hits the moving object, it "bounces" back toward the source, which also contains a receiver as well as the original transmitter. However, since the wave reflected off of the moving object, the wave is shifted as outlined by the relativistic Doppler effect.
Since the electromagnetic radiation was at a precise frequency when sent out and is at a new frequency upon its return, this can be used to calculate the velocity, v, of the target (which acts as a intermediary source).
Pulse-Doppler Radar - Weather Doppler RadarWhen watching the weather, it is this system which allows for the swirling depictions of weather patterns and, more importantly, detailed analysis of their movement.
The Pulse-Doppler radar system allows not only the determination of linear velocity, as in the case of the radar gun, but also allows for the calculation of radial velocities. It does this by sending pulses instead of beams of radiation. The shift not only in frequency, but also in carrier cycles, allows one to determine these radial velocities.
In order to achieve this, careful control of the radar system is required. The system has to be in a coherent state which allows for stability of the phases of the radiation pulses. One drawback to this is that there is a maximum speed above which the Pulse-Doppler system cannot measure radial velocity.
To understand this, consider a situation where the measurement causes the phase of the pulse to shift by 400 degrees. Mathematically, this is identical to a shift of 40 degrees, because it has gone through an entire cycle (a full 360 degrees). Speeds causing shifts such as this are called the "blind speed." It is a function of the pulsed repetition frequency of the signal, so by altering this signal meteorologists can prevent this to some degree.