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← ScienceWhich error results when truncating Fourier series terms?
A)Gibbs phenomenon oscillations near discontinuity✓
B)Aliasing from undersampled high frequencies
C)Numerical instability in discrete cosine transform
D)Spectral leakage due to windowing effects
💡 Explanation
When a Fourier series with a finite number of terms is used to approximate a discontinuous function, the **Gibbs phenomenon** creates oscillations around the discontinuity; because the truncated series struggles to accurately represent the abrupt jump, oscillations ensue rather than an ideal smooth approximation.
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