Inverse Fourier transform
Imagine you are playing with a big toy box filled with different colored toys. You take out a few of them and put them together to make a beautiful picture.
Now imagine that someone else comes along and sees your picture, but they want to know what specific toys you used to make it. They don't know how to take the toys apart and figure it out, but they have a special machine that can do it for them.
This machine is like the Fourier transform. It takes a picture (or any signal) and breaks it down into its different "toys" (or frequencies). The machine tells them how much of each "toy" they need to use to make that specific picture.
But what if they want to go the other way around? What if they have the list of "toys" and want to see what picture it makes? That's where the inverse Fourier transform comes in.
It's like taking the list of "toys" and putting them back together to recreate the picture. The inverse Fourier transform takes the list of frequencies and puts them back together in a way that creates the original signal or picture.
So, just like you put the toys back together to make a picture, the inverse Fourier transform puts the frequencies back together to make the original signal.
Now imagine that someone else comes along and sees your picture, but they want to know what specific toys you used to make it. They don't know how to take the toys apart and figure it out, but they have a special machine that can do it for them.
This machine is like the Fourier transform. It takes a picture (or any signal) and breaks it down into its different "toys" (or frequencies). The machine tells them how much of each "toy" they need to use to make that specific picture.
But what if they want to go the other way around? What if they have the list of "toys" and want to see what picture it makes? That's where the inverse Fourier transform comes in.
It's like taking the list of "toys" and putting them back together to recreate the picture. The inverse Fourier transform takes the list of frequencies and puts them back together in a way that creates the original signal or picture.
So, just like you put the toys back together to make a picture, the inverse Fourier transform puts the frequencies back together to make the original signal.