Impulse invariance

Alright kiddo, so let me explain impulse invariance in very simple terms. Imagine you have a toy car moving on a track with humps and bumps. Every time the car goes over a hump, it makes a "bump" sound. Now, suppose we want to recreate this sound using a computer. We would need to take measurements of the car's position and speed at every moment in time as it goes over the hump, and then use this information to create a sound wave that accurately represents the "bump" sound.

Impulse invariance is a method that we can use to create this sound wave. We take the measurements of the car's position and speed, and then we "sample" them - that is, we take measurements only at specific moments in time, like taking pictures with a camera. We then use mathematical equations to turn these samples into a sound wave that we can listen to.

So, impulse invariance is basically a way to turn measurements into sound waves by taking samples at specific moments in time and using math to recreate the original sound. Think of it like taking snapshots of a moving car to create a video - we're using snapshots of the car's movement to create a sound wave that accurately represents the "bump" sound.