The Fourier series is a powerful mathematical tool that expresses any periodic function as a sum of simple sine and cosine waves. By combining these basic oscillations with different frequencies, amplitudes, and phases, we can reconstruct even the most complex periodic shapes. This concept reveals that any repeating signal—no matter how irregular—can be viewed as a blend of harmonically related waves. The coefficients of the Fourier series determine how much of each frequency contributes to the

A Fourier series is a way to represent a periodic function as an infinite sum of sine and cosine terms. These trigonometric functions serve as the fundamental building blocks for many waveforms, allowing complex shapes to be reconstructed using simpler, oscillating components. The key idea is that any reasonable periodic function, no matter how jagged or irregular, can be decomposed into a sum of these smooth waves, each with a specific frequency, amplitude, and phase. This is widely used in fie

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