The Fourier series is a powerful mathematical tool that allows us to represent periodic functions as an infinite sum of sines and cosines. The idea, introduced by Joseph Fourier in the early 19th century, is that even very complex repeating waveforms can be broken down into simpler trigonometric components. Each term in the series corresponds to a frequency component of the original function, with coefficients determining the amplitude of the sine and cosine waves. This makes the Fourier series

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