Okay kiddo, so pulse-Doppler signal processing is like playing catch with a ball. You know how sometimes you throw a ball and it bounces back to you really fast, and sometimes it doesn't bounce back at all? Well, scientists have made machines that can do that too, but instead of a ball, they use sound waves.
These machines send out special sound waves, called pulses, and wait for them to bounce back. But, they don't just wait for any old bounces, they listen for Doppler shifts.
A Doppler shift is when the sound wave bounces back but it's a little bit different than when it left. This happens when the object the sound wave bounced off of is moving, so the sound wave has to travel a little further or shorter to get back to the machine.
The scientists use all of these bounces, with their Doppler shifts, to create a picture of what's around them. They can tell if something is moving or not, how fast it's moving, and even how big it is!
So, just like when you play catch with a ball and you watch it carefully to know where to reach out and catch it, scientists use pulse-Doppler signal processing to carefully listen to the sound waves bouncing back and know exactly what's around them.