Question

Why do we do fourier transform with complex terms ?

Answer 1

Fourier transforms (FT) take a signal and express it in terms of the frequencies of the waves that make up that signal. Sound is probably the easiest thing to think about when talking about Fourier transforms. If you could see sound, it would look like air molecules bouncing back and forth very quickly. But oddly enough, when you hear sound you’re not perceiving the air moving back and forth, instead you experience sound in terms of its frequencies. For example, when somebody plays middle C on a piano, you don’t feel your ear being buffeted 261 times a second (the frequency of middle C), you just hear a single tone. The buffeting movement of the air is the signal, and the tone is the Fourier transform of that signal.