Continuous Fourier transform

Imagine you have a magical toy that can turn any sound into a picture. Weird, right? But it's pretty cool!

Now, let's say you have a sound that you want to see as a picture. You play the sound into the toy and it shows you a picture made of different colored squares. But you notice that the colors and shapes keep changing really quickly!

This is kind of like what happens when we do a continuous Fourier transform. We take a sound (or any other signal) and turn it into a kind of picture. But instead of colors and shapes, we use numbers.

The Fourier transform shows us how much of each different frequency is in the sound. Think of it like breaking a sound down into different parts, like how you can break an apple pie down into crust, filling, and apples.

Now, when we say "continuous" Fourier transform, that means we're doing this for every little bit of the sound. It's like taking a whole apple pie and breaking it down slice by slice to see how much crust, filling, and apples are in each slice.

Overall, the continuous Fourier transform's main purpose is to turn a sound into a picture made of numbers that show us how much of each frequency is in the sound, and it does this by breaking the sound down into little pieces and analyzing each one.