What is Gibbs known for in Fourier analysis?
Gaussian Distribution
Gibbs Phenomenon
Pythagorean Theorem
Boolean Algebra
Answer
Gibbs is renowned in Fourier analysis for the Gibbs phenomenon, which describes the overshoot that occurs near jump discontinuities in the Fourier series of a function. This phenomenon arises due to the abrupt change in the function at these points, resulting in the oscillation of the Fourier series around the true value. The Gibbs phenomenon highlights the limitations of Fourier series in representing certain types of discontinuous functions.
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