A Fourier series is a way of expressing a periodic function as a sum of simple sine and cosine waves. The key idea is that even very complicated repeating patterns can be built from smooth oscillations with different frequencies, amplitudes, and phases. Each sine or cosine term captures a specific frequency component, and when you add enough of them together, the sum can closely approximate the original function. This decomposition reveals how much of each frequency is present, which is why Four
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