What are discrete-time systems?

A discrete-time system is like a step-by-step recipe that changes something you give it, just like when you follow instructions to build a tower with blocks.

Imagine you have a toy machine that takes in marbles one by one, and every time it gets a marble, it adds another marble to the pile. This is a discrete-time system because it works in steps, each step happens after the previous one finishes.

Think of a ball bouncing on the floor. If you watch it closely, the ball doesn’t move smoothly all the time, it goes up, then comes down, hits the floor again, and repeats. A discrete-time system is like watching that ball only at certain moments, say, every second. You don't see the whole movement, just snapshots of it.

A discrete-time system doesn’t need to be fast or fancy, it just needs to work in steps. It could be a simple machine that counts marbles, or even something like your heartbeat, counting every beat as it happens, one after the other.