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Fourier series are one of the most powerful tools in mathematics and applied science, used to represent complex periodic functions as an infinite sum of simple sine and cosine waves. At its core, a Fourier series decomposes a signal into its fundamental frequency and higher harmonics, making it essential in signal processing, electrical engineering, physics, and applied mathematics. Whether analyzing sound waves, heat transfer, vibrations, or electromagnetic signals, Fourier series provide a pre
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