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A Fourier series is a mathematical technique that breaks down a complex periodic signal into a collection of simple sine and cosine waves. One of the most famous examples is the square wave, which alternates abruptly between two values. Although a square wave appears to have sharp corners that cannot be created by smooth curves, a Fourier series can approximate it by adding together an infinite sequence of odd harmonics. As more terms are included, the approximation becomes increasingly accurate
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Fourier series provide a way to describe complicated, repeating signals using simple building blocks. The core idea is that many periodic functions can be written as a sum of sine and cosine waves with different frequencies and amplitudes. Each term captures a specific pattern of oscillation, and when these waves are added together, they recreate the original function. This perspective transforms complex shapes into combinations of smooth, regular motions, making periodic behavior easier to anal
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