The Fourier series is a mathematical method used to express any periodic function as a sum of sine and cosine functions. Even complex, non-smooth waveforms can be broken down into these simpler trigonometric components, each with its own frequency and amplitude. This decomposition allows us to analyze the frequency content of signals and is widely used in areas like physics, engineering, and audio processing. By adding enough sine and cosine terms, the Fourier series can closely approximate almo