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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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TikTokmathswithmuza
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A Fourier series expresses a periodic signal as a sum of sine and cosine waves with different frequencies, amplitudes, and phases. Even very irregular shapes can be reconstructed this way by stacking enough simple waves. A square wave is a classic example. Despite its sharp jumps, it can be built using only sine waves at odd multiples of a base frequency (1x, 3x, 5x, ...), each with decreasing amplitude. As more of these waves are added, the result gets closer to a true square wave, with sharper
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