Fourier's theorem

Fourier's theorem states that any complex, periodic function can be broken down into a series of simple sine and cosine waves with different frequencies, amplitudes, and phases. Essentially, complex signals, like sound waves or electrical signals, can be represented as a combination of basic waveforms. This decomposition allows us to analyze, process, or reconstruct signals efficiently, making Fourier's theorem fundamental in fields like signal processing, music, and communications. It reveals that all periodic signals are built from these fundamental wave patterns, simplifying the understanding and manipulation of complex phenomena.