Imagine you have a collection of simple and pure waves that never change their shape. These waves are like the clear notes you might hear from a tuning fork. Each note has its own steady rhythm and pitch. The Fourier transform works by taking a complex sound and figuring out how much of each pure note is present. Sinusoids are used because they add up in a very neat way. They do not mix into each other so when you add them, you can tell exactly which notes are there. This makes it easier to break down and understand any complicated signal.
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Imagine you have a collection of simple and pure waves that never change their shape. These waves are like the clear notes you might hear from a tuning fork. Each note has its own steady rhythm and pitch. The Fourier transform works by taking a complex sound and figuring out how much of each pure note is present. Sinusoids are used because they add up in a very neat way. They do not mix into each other so when you add them, you can tell exactly which notes are there. This makes it easier to break down and understand any complicated signal.