Fourier's series expansion

Fourier's series expansion is a mathematical method that breaks down complex periodic signals into a sum of simpler sine and cosine waves. Think of any repeating pattern—like a sound wave or a signal—as a combination of smooth, oscillating components. By expressing it this way, we can analyze, process, or recreate the original pattern more effectively. Essentially, Fourier's series reveals the fundamental "building blocks" of a wave, making it easier to study the structure of signals in engineering, physics, and mathematics.